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Prof. Dr.

Christian Rohde

Head of Group
Institute of Applied Analysis and Numerical Simulation
Chair of Applied Mathematics

Contact

+49 711 685-65524
+49 711 685-65599
Email

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.131

Consultation

Friday, 10:30-11:30

Publications

2019
1. J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws,” 2019.
  - BibTeX
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  @techreport{GiesselmannMeyerRohde2019, abstract = {In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatial-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithms.}, author = {Giesselmann, J. and Meyer, F. and Rohde, C.}, title = {A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws}, url = {https://arxiv.org/abs/1902.05375}, year = 2019 }
2. J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method.,” IMA J. Numer. Anal., 2019.
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  @article{giesselmannMeyerRohde19, abstract = {In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the Stochastic Galerkin method and for the spatial-temporal discretisation of the Stochastic Galerkin system a Runge-Kutta Discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos \cite{dafermos2005hyperbolic}, this leads to computable error bounds for the space-stochastic discretisation error. \\ Moreover, it turns out that the error estimator admits a splitting into one part representing the spatial error, and a remaining term, which can be interpreted as the stochastic error. This decomposition allows us to balance the errors arising from spatial and stochastic discretisation. We conclude with some numerical examples confirming the theoretical findings. }, author = {Giesselmann, J. and Meyer, F. and Rohde, C.}, doi = {10.1093/imanum/drz004}, journal = {IMA J. Numer. Anal.}, owner = {meyerfn}, title = {A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method.}, url = {https://dx.doi.org/10.1093/imanum/drz004}, year = 2019 }
2018
1. S. Fechter, C.-D. Munz, C. Rohde, and C. Zeiler, “Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension,” Comput. & Fluids, vol. 169, pp. 169–185, 2018.
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  @article{fechter2018approximate, author = {Fechter, Stefan and Munz, Claus-Dieter and Rohde, Christian and Zeiler, Christoph}, doi = {http://dx.doi.org/10.1016/j.compfluid.2017.03.026}, journal = {Comput. \& Fluids}, owner = {szur}, pages = {169-185}, title = {Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension}, url = {http://www.sciencedirect.com/science/article/pii/S004579301730107X}, volume = 169, year = 2018 }
2. T. Kuhn, J. Dürrwächter, A. Beck, C.-D. Munz, F. Meyer, and C. Rohde, “Uncertainty Quantification for Direct Aeroacoustic Simulations of Cavity Flows,” Journal of Theoretical and Computational Acoustics, 2018.
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  @article{kuhn2018uncertainty, abstract = {We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The so-called Rossiter feedback requires a direct numerical computation of the acoustic noise, which solves hydrodynamics and acoustics simultaneously, in order to capture the interaction of acoustic waves and the hydrodynamics of the flow. Due to the large bandwidth of spatial and temporal scales, a high order numerical scheme with low dissipation and dispersion error is necessary to preserve important small scale information. Therefore, the open-source CFD solver FLEXI, which is based on a high-order discontinuous Galerkin spectral element method, is used to perform the aforementioned direct simulations of an open cavity configuration with a laminar upstream boundary layer. To analyse the precision of the deterministic cavity simulation with respect to random input parameters we establish a framework for uncertainty quantification. In particular, a non-intrusive spectral projection method with Legendre and Hermite polynomial basis functions is employed in order to treat uniform and normal probability distributions of the uncertain input. The results indicate a strong, non-linear dependency of the acoustic feedback mechanism on the investigated uncertain input parameters. An analysis of the stochastic results offers new insights into the noise generation process of open cavity flows and reveals the strength of the implemented uncertainty quantification framework.}, author = {Kuhn, T. and D\"{u}rrw\"{a}chter, J. and Beck, A. and Munz, C.-D. and Meyer, F. and Rohde, C.}, doi = {10.1142/S2591728518500445}, journal = {Journal of Theoretical and Computational Acoustics}, owner = {meyerfn}, title = {Uncertainty Quantification for Direct Aeroacoustic Simulations of Cavity Flows}, url = {https://doi.org/10.1142/S2591728518500445}, year = 2018 }
3. V. Sharanyaa, G. P. R. Sekhara, and C. Rohde, “The low surface Péclet number regime for surfactant-laden viscous droplets: Influence of surfactant concentration, interfacial slip effects and cross migration,” International Journal of Multiphase Flow, no. 107, pp. 82–103, 2018.
  - BibTeX
  @article{sharanyaa2018surface, author = {Sharanyaa, V. and Sekhara, G.P. Raja and Rohde, Christian}, doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.008}, journal = {International Journal of Multiphase Flow}, month = oct, number = 107, pages = {82-103}, title = {The low surface Péclet number regime for surfactant-laden viscous droplets: Influence of surfactant concentration, interfacial slip effects and cross migration}, year = 2018 }
4. A. Armiti-Juber and C. Rohde, “On Darcy-and Brinkman-Type Models for Two-Phase Flow in Asymptotically Flat Domains,” Computational Geosciences, pp. 1–19, 2018.
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  @article{armitijuber2017darcyand, author = {Armiti-Juber, A. and Rohde, C.}, doi = {10.1007/s10596-018-9756-2}, journal = {Computational Geosciences}, owner = {seusdd}, pages = {1-19}, title = {On Darcy-and Brinkman-Type Models for Two-Phase Flow in Asymptotically Flat Domains}, url = {https://link.springer.com/article/10.1007/s10596-018-9756-2}, year = 2018 }
5. C. Rohde and C. Zeiler, “On Riemann Solvers and Kinetic Relations for Isothermal Two-Phase Flows with Surface Tension,” Z. Angew. Math. Phys., p. 69:76, 2018.
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  @article{rohde2018riemann, author = {Rohde, C. and Zeiler, C.}, journal = {Z. Angew. Math. Phys.}, owner = {szur}, pages = {69:76}, title = {On Riemann Solvers and Kinetic Relations for Isothermal Two-Phase Flows with Surface Tension}, url = {https://doi.org/10.1007/s00033-018-0958-1}, year = 2018 }
6. C. Chalons, J. Magiera, C. Rohde, and M. Wiebe, “A Finite-Volume Tracking Scheme for Two-Phase Compressible Flow,” in Springer Proc. Math. Stat., Cham, 2018, pp. 309--322.
  - BibTeX
  @inproceedings{chalons.magiera.ea:finite:2018, abstract = {We propose a finite-volume tracking method in multiple space dimensions to approximate weak solutions of the hydromechanical equations that allow two-phase behavior. The method relies on a moving mesh ansatz such that the phase boundary is represented as a sharp interface without any artificial smearing. At the interface, an approximate solver is applied, such that the exact Riemann solution is not required. From precedent work, it is known that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme, we test it on various situations for liquid--vapor flow.}, address = {Cham}, author = {Chalons, Christophe and Magiera, Jim and Rohde, Christian and Wiebe, Maria}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, doi = {10.1007/978-3-319-91545-6_25}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91545-6}, journal = {Springer Proc. Math. Stat.}, pages = {309--322}, publisher = {Springer International Publishing}, title = {A Finite-Volume Tracking Scheme for Two-Phase Compressible Flow}, year = 2018 }
7. G. P. Raja Sekhar, V. Sharanya, and C. Rohde, “Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface P�clet number,” erscheint bei Int. J. Multiph. Flow, 2018.
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  @article{rajasekhar2018effect, abstract = {The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface P\'eclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface P\'eclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surface P\'eclet number. Further instances corresponding to a given ambient flow as uniform flow, Couette flow, Poiseuille flow are analyzed. Moreover, it is observed that, a surfactant-induced cross-stream migration of the drop occur towards the centre-line in both Couette flow and Poiseuille flow cases. The variation of the drag force and migration velocity is computed for different parameters such as P\'eclet number, Marangoni number etc.}, author = {Raja Sekhar, G. P. and Sharanya, V. and Rohde, Christian}, journal = {erscheint bei Int. J. Multiph. Flow}, owner = {szur}, title = {Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface P�clet number}, url = {http://arxiv.org/abs/1609.03410}, year = 2018 }
8. A. Beck, J. Dürrwächter, T. Kuhn, F. Meyer, C.-D. Munz, and C. Rohde, “$hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Flows,” 2018.
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  @techreport{meyer2018hp, abstract = {We propose a novel $hp$-Multilevel Monte Carlo method for the quantification of uncertainties in compressible flows using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes jointly with an increasing polynomial degree for the ansatz space. It allows for a very large range of resolutions in the physical space and thus an efficient decrease of the statistical error. We prove that the overall complexity of the $hp$-Multilevel Monte Carlo method to compute the mean field with prescribed accuracy is of quadratic order with respect to the accuracy. We also propose a novel and simple approach to estimate a lower confidence bound for the optimal number of samples per level, which helps to prevent overshooting the optimal number of samples. The method is in particular adapted to the needs of high-performance computing. Our theoretical results are verified by numerical experiments for the two dimensional compressible Navier-Stokes equations. In particular we consider a cavity flow problem from computational acoustics, demonstrating that the method is suitable to handle complex engineering problems.}, author = {Beck, A. and D\"{u}rrw\"{a}chter, J. and Kuhn, T. and Meyer, F. and Munz, C.-D. and Rohde, C.}, owner = {meyerfn}, title = {$hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Flows}, url = {https://arxiv.org/abs/1808.10626}, year = 2018 }
9. J. Magiera and C. Rohde, “A Particle-Based Multiscale Solver for Compressible Liquid--Vapor Flow,” in Springer Proc. Math. Stat., Cham, 2018, pp. 291--304.
  - BibTeX
  @inproceedings{magiera.rohde:particle:2018, abstract = {To describe complex flow systems accurately, it is in many cases important to account for the properties of fluid flows on a microscopic scale. In this work, we focus on the description of liquid--vapor flow with a sharp interface between the phases. The local phase dynamics at the interface can be interpreted as a Riemann problem for which we develop a multiscale solver in the spirit of the heterogeneous multiscale method (HMM) [7], using a particle-based microscale model to augment the macroscopic two-phase flow system. The application of a microscale model makes it possible to use the intrinsic properties of the fluid at the microscale, instead of formulating (ad hoc) constitutive relations.}, address = {Cham}, author = {Magiera, Jim and Rohde, Christian}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems II}, doi = {10.1007/978-3-319-91548-7_23}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91548-7}, journal = {Springer Proc. Math. Stat.}, pages = {291--304}, publisher = {Springer International Publishing}, title = {A Particle-Based Multiscale Solver for Compressible Liquid--Vapor Flow}, year = 2018 }
2017
1. C. Rohde, “Fully Resolved Compressible Two-Phase Flow: Modelling, Analytical and Numerical Issues,” 2017.
  - BibTeX
  @article{rohde2017fully, author = {Rohde, C.}, owner = {szur}, title = {Fully Resolved Compressible Two-Phase Flow: Modelling, Analytical and Numerical Issues}, year = 2017 }
2. M. Köppel, I. Kröker, and C. Rohde, “Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media,” Comput. Geosci., vol. 21, pp. 807–832, 2017.
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  @article{koppel2017intrusive, author = {Köppel, Markus and Kröker, Ilja and Rohde, Christian}, doi = {10.1007/s10596-017-9662-z}, journal = {Comput. Geosci.}, owner = {szur}, pages = {807-832}, title = {Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media}, url = {https://link.springer.com/article/10.1007%2Fs10596-017-9662-z}, volume = 21, year = 2017 }
3. C. Chalons, C. Rohde, and M. Wiebe, “A Finite Volume Method for Undercompressive Shock Waves in Two Space Dimensions,” ESAIM Math. Model. Numer. Anal., vol. 51, no. 5, pp. 1987–2015, 2017.
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  @article{chalons2017finite, author = {Chalons, Christophe. and Rohde, Christian and Wiebe, Maria}, doi = {https://doi.org/10.1051/m2an/2017027}, journal = {ESAIM Math. Model. Numer. Anal.}, month = {September-October 2017}, number = 5, owner = {seusdd}, pages = {1987-2015}, title = {A Finite Volume Method for Undercompressive Shock Waves in Two Space Dimensions}, url = {https://www.esaim-m2an.org/component/article?access=doi&doi=10.1051/m2an/2017027}, volume = 51, year = 2017 }
4. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” 2017.
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  @techreport{koppel2017comparison, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods� advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K\{"o}ppel, M. and Franzelin, F. and Kr\{"o}ker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, B. and Nowak, W. and Pfl\{"u}ger, D. and Rohde, C.}, owner = {santinge}, title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759}, year = 2017 }
5. D. Seus, F. A. Radu, and C. Rohde, “A linear domain decomposition method for two-phase flow in porous media,” 2017.
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  @inproceedings{seus2017linear, author = {Seus, David and Radu, Florin A. and Rohde, Christian}, doi = {arXiv:1712.04869}, owner = {seusdd}, title = {A linear domain decomposition method for two-phase flow in porous media}, url = {http://arxiv.org/abs/1712.04869}, year = 2017 }
2016
1. M. Dumbser, G. Gassner, C. Rohde, and S. Roller, “Preface to the special issue ``Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations’’,” Appl. Math. Comput., vol. 272, no. part 2, pp. 235--236, 2016.
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  @article{dumbser2016preface, author = {Dumbser, Michael and Gassner, Gregor and Rohde, Christian and Roller, Sabine}, doi = {10.1016/j.amc.2015.11.023}, fjournal = {Applied Mathematics and Computation}, issn = {0096-3003}, journal = {Appl. Math. Comput.}, mrclass = {Preliminary Data}, mrnumber = {3421104}, number = {part 2}, owner = {joosde}, pages = {235--236}, title = {Preface to the special issue ``{R}ecent {A}dvances in {N}umerical {M}ethods for {H}yperbolic {P}artial {D}ifferential {E}quations''}, url = {http://dx.doi.org/10.1016/j.amc.2015.11.023}, volume = 272, year = 2016 }
2. J. Magiera, C. Rohde, and I. Rybak, “A hyperbolic-elliptic model problem for coupled surface-subsurface flow,” Transp. Porous Media, vol. 114, no. 2, pp. 425–455, 2016.
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  @article{magiera2016hyperbolicelliptic, author = {Magiera, J. and Rohde, C. and Rybak, I.}, doi = {10.1007/S11242-015-0548-Z}, journal = {Transp. Porous Media}, number = 2, owner = {ingrid}, pages = {425-455}, title = {A hyperbolic-elliptic model problem for coupled surface-subsurface flow}, url = {http://dx.doi.org/10.1007/s11242-015-0548-z}, volume = 114, year = 2016 }
3. V. Sharanya, G. P. Raja Sekhar, and C. Rohde, “Bed of polydisperse viscous spherical drops under thermocapillary effects,” Z. Angew. Math. Phys., vol. 67, no. 4, p. 101, 2016.
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  @article{sharanya2016polydisperse, abstract = {Viscous flow past an ensemble of polydisperse spherical drops is investigated under thermocapillary effects. We assume that the collection of spherical drops behaves as a porous media and estimates the hydrodynamic interactions analytically via the so- called cell model that is defined around a specific representative particle. In this method, the hydrodynamic interactions are assumed to be accounted by suitable boundary conditions on a fictitious fluid envelope surrounding the representative particle. The force calculated on this representative particle will then be extended to a bed of spherical drops visualized as a Darcy porous bed. Thus, the ``effective bed permeability'' of such a porous bed will be computed as a function of various parameters and then will be compared with Carman--Kozeny relation. We use cell model approach to a packed bed of spherical drops of uniform size (monodisperse spherical drops) and then extend the work for a packed bed of polydisperse spherical drops, for a specific parameters. Our results show a good agreement with the Carman--Kozeny relation for the case of monodisperse spherical drops. The prediction of overall bed permeability using our present model agrees well with the Carman--Kozeny relation when the packing size distribution is narrow, whereas a small deviation can be noted when the size distribution becomes broader.}, author = {Sharanya, V. and Raja Sekhar, G. P. and Rohde, Christian}, doi = {10.1007/s00033-016-0699-y}, issn = {1420-9039}, journal = {Z. Angew. Math. Phys.}, number = 4, owner = {szur}, pages = 101, title = {Bed of polydisperse viscous spherical drops under thermocapillary effects}, url = {http://dx.doi.org/10.1007/s00033-016-0699-y}, volume = 67, year = 2016 }
4. M. Redeker, I. S. Pop, and C. Rohde, “Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media,” IMA J. Appl. Math., vol. 81(5), pp. 898–939, 2016.
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  @article{redeker2016upscaling, abstract = {We consider a porous medium with a pore space that is completely filled by three different phases: two immiscible fluids (say water and oil) and a solid phase. One fluid phase contains dissolved ions, which can precipitate at the pore boundary to form the solid phase. The reverse process of dissolution, is also possible. Consequently, the solid phase changes in time; its variation is not known a-priori. The second fluid contains no solute and has no interaction with the solid phase. Starting from a standard sharp interface model for the pore-scale dynamics we develop a diffuse interface approach that accounts for the time-dependent spatial distribution of the three species and the overall concentration of the solute. Basic analytical results for this model are presented, including the well posedness of the phase field component of the model. Next we apply matched asymptotic techniques to show that the diffuse interface model converges to the sharp interface one. Further, homogenization is applied to derive a new two-scale model that is valid at the Darcy scale. This leads to a parabolic reaction-diffusion system in a medium with variable, concentration dependent porosity. The diffuse interface approach allows describing the variation in the porosity as phase field type equations at the pore-scale. The last part of the paper presents an efficient numerical scheme to approximate the solution of the two-scale model. This scheme has as starting point the algorithm in [M. Redeker and C. Eck. A fast and accurate adaptive solution strategy for two-scale models with continuous inter-scale dependencies. J. Comput. Phys., 240:268�283, 2013]. After some test cases validating the method, we finally present computations for several realistic scenarios. The results demonstrate the interdependence of the change of the pore structure due to precepitaion/dissolution and the evolution of the Darcy scale concentration of the dissolved particles in the one fluid.}, author = {Redeker, Magnus and Pop, Iuliu Sorin and Rohde, Christian}, doi = {https://doi.org/10.1093/imamat/hxw023}, journal = {IMA J. Appl. Math.}, owner = {redeker}, pages = {898-939}, title = {Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media}, url = {https://academic.oup.com/imamat/article-lookup/doi/10.1093/imamat/hxw023}, volume = {81(5)}, year = 2016 }
5. I. Dragomirescu, K. Eisenschmidt, C. Rohde, and B. Weigand, “Perturbation solutions for the finite radially symmetric Stefan problem,” Inter. J. Thermal Sci., vol. 104, pp. 386–395, 2016.
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  @article{dragomirescu2016perturbation, author = {Dragomirescu, Ioana and Eisenschmidt, Kathrin and Rohde, Christian and Weigand, Bernhard}, doi = {https://doi.org/10.1016/j.ijthermalsci.2016.01.019}, journal = {Inter. J. Thermal Sci.}, owner = {joosde}, pages = {386-395}, title = {Perturbation solutions for the finite radially symmetric Stefan problem}, url = {http://www.sciencedirect.com/science/article/pii/S1290072916000326}, volume = 104, year = 2016 }
6. M. Köppel and C. Rohde, “Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media,” PAMM Proc. Appl. Math. Mech., vol. 16, no. 1, pp. 749–750, 2016.
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  @article{koppel2016uncertainty, author = {K{\"o}ppel, Markus and Rohde, Christian}, doi = {10.1002/pamm.201610363}, journal = {PAMM Proc. Appl. Math. Mech.}, number = 1, owner = {seusdd}, pages = {749–750}, publisher = {WILEY-VCH Verlag}, title = {Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media}, url = {http://onlinelibrary.wiley.com/doi/10.1002/pamm.201610363/abstract}, volume = 16, year = 2016 }
7. D. Diehl, J. Kremser, D. Kröner, and C. Rohde, “Numerical Solution of Navier-Stokes-Korteweg Systems by Local Discontinuous Galerkin Methods in Multiple Space Dimensions,” Appl. Math. Comput., vol. 272, Part 2, pp. 309–335, 2016.
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  @article{diehl2016numerical, author = {Diehl, D. and Kremser, J. and Kr{\"o}ner, D. and Rohde, C.}, doi = {10.1016/j.amc.2015.09.080}, journal = {Appl. Math. Comput.}, owner = {seusdd}, pages = {309-335}, title = {Numerical Solution of Navier-Stokes-Korteweg Systems by Local Discontinuous Galerkin Methods in Multiple Space Dimensions}, url = {http://www.sciencedirect.com/science/article/pii/S0096300315013181}, volume = {272, Part 2}, year = 2016 }
8. R. M. Colombo, P. G. LeFloch, and C. Rohde, “Hyperbolic techniques in Modelling, Analysis and Numerics,” Oberwolfach Reports, vol. 13, pp. 1683–1751, 2016.
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  @article{colombo2016hyperbolic, author = {Colombo, R. M. and LeFloch, P. G. and Rohde, C.}, doi = {10.4171/OWR/2016/30}, journal = {Oberwolfach Reports}, note = {Abstracts from the workshop held June 19--25, 2016, Organized by Rinaldo M. Colombo, Philippe G. LeFloch and Christian Rohde}, owner = {szur}, pages = {1683-1751}, title = {Hyperbolic techniques in Modelling, Analysis and Numerics}, url = {http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=13&iss=2&rank=12}, volume = 13, year = 2016 }
9. F. Betancourt and C. Rohde, “Finite-Volume Schemes for Friedrichs Systems with Involutions,” App. Math. Comput., vol. 272, Part 2, pp. 420–439, 2016.
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  @article{betancourt2016finitevolume, author = {Betancourt, F. and Rohde, C.}, doi = {10.1016/j.amc.2015.03.050}, journal = {App. Math. Comput.}, owner = {seusdd}, pages = {420-439}, title = {{Finite-Volume Schemes for Friedrichs Systems with Involutions}}, url = {http://www.sciencedirect.com/science/article/pii/S0096300315003641}, volume = {272, Part 2}, year = 2016 }
2015
1. I. Rybak, J. Magiera, R. Helmig, and C. Rohde, “Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems,” Comput. Geosci., vol. 19, pp. 299--309, 2015.
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  @article{rybak2015multirate, author = {Rybak, I. and Magiera, J. and Helmig, R. and Rohde, C.}, doi = {10.1007/s10596-015-9469-8}, journal = {Comput. Geosci.}, owner = {rybak}, pages = {299--309}, title = {Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems}, url = {http://link.springer.com/article/10.1007/s10596-015-9469-8}, volume = 19, year = 2015 }
2. C. Rohde and C. Zeiler, “A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension,” Appl. Numer. Math., vol. 95, pp. 267--279, 2015.
  - BibTeX
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  @article{rohde2015relaxation, abstract = {The dynamics of two-phase flows depend crucially on interfacial effects like surface tension and phase transition. A numerical method for compressible inviscid flows is proposed that accounts in particular for these two effects. The approach relies on the solution of Riemann-like problems across the interface that separates the liquid and the vapour phase. Since the analytical solutions of the Riemann problems are only known in particular cases an approximative Riemann solver for arbitrary settings is constructed. The approximative solutions rely on the relaxation technique. The local well-posedness of the approximative solver is proven. Finally we present numerical experiments for radially symmetric configurations that underline the reliability and efficiency of the numerical scheme.}, author = {Rohde, C. and Zeiler, C.}, doi = {10.1016/j.apnum.2014.05.001}, issn = {0168-9274}, journal = {Appl. Numer. Math.}, mrclass = {65M25 (76N99 76T10)}, mrnumber = {3349699}, owner = {seusdd}, pages = {267--279}, title = {A relaxation {R}iemann solver for compressible two-phase flow with phase transition and surface tension}, url = {http://dx.doi.org/10.1016/j.apnum.2014.05.001}, volume = 95, year = 2015 }
3. F. Kissling and C. Rohde, “The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case,” Multiscale Model. Simul., vol. 13 no. 4, pp. 1507–1541, 2015.
  - BibTeX
  - Link
  @article{kissling2015computation, author = {Kissling, F. and Rohde, C.}, doi = {10.1137/120899236}, journal = {Multiscale Model. Simul.}, owner = {seusdd}, pages = {1507-1541}, title = {The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case}, url = {http://epubs.siam.org/doi/abs/10.1137/120899236}, volume = {13 no. 4}, year = 2015 }
4. J. Neusser, C. Rohde, and V. Schleper, “Relaxation of the Navier-Stokes-Korteweg Equations for Compressible Two-Phase Flow with Phase Transition,” J. Numer. Methods Fluids, vol. 79, pp. 615–639, 2015.
  - BibTeX
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  @article{neusser2015relaxation, author = {Neusser, J. and Rohde, C. and Schleper, V.}, doi = {10.1002/fld.4065}, journal = {J. Numer. Methods Fluids}, pages = {615-639}, title = {{Relaxation of the Navier-Stokes-Korteweg Equations for Compressible Two-Phase Flow with Phase Transition}}, url = {http://onlinelibrary.wiley.com/doi/10.1002/fld.4065/abstract}, volume = 79, year = 2015 }
5. J. Neusser, C. Rohde, and V. Schleper, “Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition,” J. Numer. Meth. Fluids, vol. 79, no. 12, pp. 615–639, 2015.
  - BibTeX
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  @article{neusser2015relaxed, abstract = {The Navier�Stokes�Korteweg (NSK) system is a classical diffuse-interface model for compressible two-phase flow. However, the direct numerical simulation based on the NSK system is quite expensive and in some cases even not possible. We propose a lower-order relaxation of the NSK system with hyperbolic first-order part. This allows applying numerical methods for hyperbolic conservation laws and removing some of the difficulties of the original NSK system. To illustrate the new ansatz, we first present a local discontinuous Galerkin method in one and two spatial dimensions. It is shown that we can compute initial boundary value problems with realistic density ratios and perform stable computations for small interfacial widths. Second, we show that it is possible to construct a semi-discrete finite-volume scheme that satisfies a discrete entropy inequality.}, author = {Neusser, J. and Rohde, C. and Schleper, V.}, doi = {10.1002/fld.4065}, journal = {J. Numer. Meth. Fluids}, month = {December}, number = 12, owner = {schleper}, pages = {615-639}, title = {Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition}, url = {http://onlinelibrary.wiley.com/doi/10.1002/fld.4065/full}, volume = 79, year = 2015 }
6. I. Kröker, W. Nowak, and C. Rohde, “A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems,” Comput. Geosci., vol. 19, no. 2, pp. 269--284, 2015.
  - BibTeX
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  @article{kroker2015stochastically, author = {Kröker, Ilja and Nowak, Wolfgang and Rohde, Christian}, doi = {10.1007/s10596-014-9464-5}, issn = {1420-0597}, journal = {Comput. Geosci.}, language = {English}, number = 2, owner = {seusdd}, pages = {269--284}, publisher = {Springer International Publishing}, title = {A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems}, url = {http://dx.doi.org/10.1007/s10596-014-9464-5}, volume = 19, year = 2015 }
2014
1. R. Bürger, I. Kröker, and C. Rohde, “A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit,” ZAMM Z. Angew. Math. Mech., vol. 94, no. 10, pp. 793–817, 2014.
  - BibTeX
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  @article{burger2014hybrid, author = {B{\"u}rger, R. and Kr{\"o}ker, I. and Rohde, C.}, doi = {10.1002/zamm.201200174}, journal = {ZAMM Z. Angew. Math. Mech.}, number = 10, owner = {seusdd}, pages = {793-817}, title = {A hybrid stochastic {G}alerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit}, url = {http://dx.doi.org/10.1002/zamm.201200174}, volume = 94, year = 2014 }
2. W. Ehlers, R. Helmig, and C. Rohde, “Editorial: Deformation and transport phenomena in porous media,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f�r Angewandte Mathematik und Mechanik, vol. 94, no. 7–8, pp. 559--559, 2014.
  - BibTeX
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  @article{ehlers2014editorial, author = {Ehlers, Wolfgang and Helmig, Rainer and Rohde, Christian}, doi = {10.1002/zamm.201400559}, issn = {1521-4001}, journal = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f�r Angewandte Mathematik und Mechanik}, number = {7-8}, owner = {seusdd}, pages = {559--559}, publisher = {WILEY-VCH Verlag}, title = {Editorial: Deformation and transport phenomena in porous media}, url = {http://dx.doi.org/10.1002/zamm.201400559}, volume = 94, year = 2014 }
3. C. Chalons, P. Engel, and C. Rohde, “A Conservative and Convergent Scheme for Undercompressive Shock Waves,” SIAM J. Numer. Anal., vol. 52, no. 1, pp. 554–579, 2014.
  - BibTeX
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  @article{chalons2014conservative, author = {Chalons, C. and Engel, P. and Rohde, C.}, journal = {SIAM J. Numer. Anal.}, note = {accepted}, number = 1, owner = {ingrid}, pages = {554-579}, title = {A Conservative and Convergent Scheme for Undercompressive Shock Waves}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=732}, volume = 52, year = 2014 }
4. P. Engel, A. Viorel, and C. Rohde, “A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics,” Port. Math., vol. 70, no. 4, pp. 319–344, 2014.
  - BibTeX
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  @article{engel2014loworder, author = {Engel, P. and Viorel, A. and Rohde, C.}, journal = {Port. Math.}, number = 4, pages = {319-344}, title = {A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=723}, volume = 70, year = 2014 }
5. S. Fechter, C. Zeiler, C.-D. Munz, and C. Rohde, “Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin Method,” in ILASS�Europe, 26th European Conference on Liquid Atomization and Spray Systems, 2014.
  - BibTeX
  @inproceedings{fechter2014simulation, author = {Fechter, Stefan and Zeiler, Christoph and Munz, Claus-Dieter and Rohde, Christian}, booktitle = {ILASS�Europe, 26th European Conference on Liquid Atomization and Spray Systems}, owner = {seusdd}, title = {Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin Method}, year = 2014 }
6. A. Armiti-Juber and C. Rohde, “Almost Parallel Flows in Porous Media,” in Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, vol. 78, J. Fuhrmann, M. Ohlberger, and C. Rohde, Eds. Springer International Publishing, 2014, pp. 873–881.
  - BibTeX
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  @incollection{armitijuber2014almost, author = {Armiti-Juber, A. and Rohde, C.}, booktitle = {Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems}, doi = {10.1007/978-3-319-05591-6_88}, editor = {Fuhrmann, J�rgen and Ohlberger, Mario and Rohde, Christian}, owner = {seusdd}, pages = {873-881}, publisher = {Springer International Publishing}, title = {Almost Parallel Flows in Porous Media}, url = {http://dx.doi.org/10.1007/978-3-319-05591-6_88}, volume = 78, year = 2014 }
7. A. Corli, C. Rohde, and V. Schleper, “Parabolic approximations of diffusive-dispersive equations.,” J. Math. Anal. Appl., vol. 414, pp. 773–798, 2014.
  - BibTeX
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  @article{corli2014parabolic, author = {Corli, A. and Rohde, C. and Schleper, V.}, journal = {J. Math. Anal. Appl.}, owner = {schleper}, pages = {773-798}, title = {Parabolic approximations of diffusive-dispersive equations.}, url = {http://dx.doi.org/10.1016/j.jmaa.2014.01.049}, volume = 414, year = 2014 }
2013
1. K. Eisenschmidt, P. Rauschenberger, C. Rohde, and B. Weigand, “Modelling of freezing processes in super-cooled droplets on sub-grid scale,” in ILASS�Europe, 25th European Conference on Liquid Atomization and Spray Systems, 2013.
  - BibTeX
  @inproceedings{eisenschmidt2013modelling, author = {Eisenschmidt, K. and Rauschenberger, P. and Rohde, C. and Weigand, B.}, booktitle = {ILASS�Europe, 25th European Conference on Liquid Atomization and Spray Systems}, title = {Modelling of freezing processes in super-cooled droplets on sub-grid scale}, year = 2013 }
2. C. Rohde, W. Wang, and F. Xie, “Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model,” Mathematical Models and Methods in Applied Sciences, vol. 23, no. 03, pp. 441--469, 2013.
  - BibTeX
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  @article{rohde2013decay, author = {Rohde, Christian and Wang, Wenjun and Xie, Feng}, doi = {10.1142/S0218202512500522}, eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218202512500522}, journal = {Mathematical Models and Methods in Applied Sciences}, number = 03, pages = {441--469}, title = {Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model}, url = {http://www.worldscientific.com/doi/abs/10.1142/S0218202512500522}, volume = 23, year = 2013 }
3. C. Rohde, W. Wang, and F. Xie, “Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves,” Communications on Pure and Applied Analysis, vol. 12, no. 5, pp. 2145--2171, 2013.
  - BibTeX
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  @article{rohde2013hyperbolichyperbolic, author = {Rohde, Christian and Wang, Wenjun and Xie, Feng}, doi = {10.3934/cpaa.2013.12.2145}, journal = {Communications on Pure and Applied Analysis}, number = 5, pages = {2145--2171}, title = {Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves}, url = {http://dx.doi.org/10.3934/cpaa.2013.12.2145}, volume = 12, year = 2013 }
2012
1. A. Corli and C. Rohde, “Singular limits for a parabolic-elliptic regularization of scalar conservation laws,” J. Differential Equations, vol. 253, no. 5, pp. 1399--1421, 2012.
  - BibTeX
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  @article{corli2012singular, author = {Corli, Andrea and Rohde, Christian}, coden = {JDEQAK}, doi = {10.1016/j.jde.2012.05.006}, fjournal = {Journal of Differential Equations}, issn = {0022-0396}, journal = {J. Differential Equations}, mrclass = {35L65 (35C07 35L67)}, mrnumber = {2927386}, number = 5, owner = {szur}, pages = {1399--1421}, title = {Singular limits for a parabolic-elliptic regularization of scalar conservation laws}, url = {http://dx.doi.org/10.1016/j.jde.2012.05.006}, volume = 253, year = 2012 }
2. W. Dreyer, J. Giesselmann, C. Kraus, and C. Rohde, “Asymptotic Analysis for Korteweg Models,” Interfaces Free Bound., vol. 14, pp. 105–143, 2012.
  - BibTeX
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  @article{dreyer2012asymptotic, author = {Dreyer, Wolfgang and Giesselmann, Jan and Kraus, Christiane and Rohde, Christian}, journal = {Interfaces Free Bound.}, owner = {Jan}, pages = {105 - 143}, title = {Asymptotic Analysis for Korteweg Models}, url = {http://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=14&iss=1&rank=4}, volume = 14, year = 2012 }
3. P. Engel and C. Rohde, “On the Space-Time Expansion Discontinuous Galerkin Method,” in Hyperbolic Problems: Theory, Numerics and Applications, 2012, pp. 406--414.
  - BibTeX
  @inproceedings{engel2012spacetime, author = {Engel, Patrick and Rohde, Christian}, booktitle = {Hyperbolic Problems: Theory, Numerics and Applications}, editor = {Li, T. and Jiang, S.}, pages = {406--414}, series = {Series in Contemporary Applied Mathematics}, title = {On the Space-Time Expansion Discontinuous Galerkin Method}, year = 2012 }
4. F. Jaegle, C. Rohde, and C. Zeiler, “A multiscale method for compressible liquid-vapor flow with surface tension,” ESAIM: Proc., vol. 38, pp. 387–408, 2012.
  - BibTeX
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  @article{jaegle2012multiscale, abstract = {Discontinuous Galerkin methods have become a powerful tool for approximation the solution of compressible ?ow problems. Their direct use for two-phase ?ow problems with phase transformation is not straightforward because this type of ?ows requires a detailed tracking of the phase front. We consider the fronts in this contribution as sharp interfaces and propose a novel multiscale approach. It combines an e?cient high-order Discontinuous Galerkin solver for the computation in the bulk phases on the macro-scale with the use of a generalized Riemann solver on the micro-scale. The Riemann solver takes into account the e?ects of moderate surface tension via the curvature of the sharp interface as well as phase transformation. First numerical experiments in three space dimensions underline the overall performance of the method.}, author = {Jaegle, Felix and Rohde, Christian and Zeiler, Christoph}, doi = {10.1051/proc/201238022}, journal = {ESAIM: Proc.}, owner = {seusdd}, pages = {387-408}, title = {A multiscale method for compressible liquid-vapor flow with surface tension}, url = {http://dx.doi.org/10.1051/proc/201238022}, volume = 38, year = 2012 }
5. F. Kissling and C. Rohde, “Numerical Simulation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method,” in Hyperbolic Problems: Theory, Numerics and Applications, 2012, pp. 469--478.
  - BibTeX
  @conference{kissling2012numerical, author = {Kissling, F. and Rohde, C.}, booktitle = {Hyperbolic Problems: Theory, Numerics and Applications}, editor = {Li, T. and Jiang, S.}, owner = {kissling}, pages = {469--478}, series = {Series in Contemporary Applied Mathematics}, title = {Numerical {S}imulation of {N}onclassical {S}hock {W}aves in {P}orous {M}edia with a {H}eterogeneous {M}ultiscale {M}ethod}, year = 2012 }
6. I. Kröker and C. Rohde, “Finite volume schemes for hyperbolic balance laws with multiplicative noise,” Appl. Numer. Math., vol. 62, no. 4, pp. 441--456, 2012.
  - BibTeX
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  @article{kroker2012finite, author = {Kr{\"o}ker, I. and Rohde, C.}, coden = {ANMAEL}, doi = {10.1016/j.apnum.2011.01.011}, fjournal = {Applied Numerical Mathematics. An IMACS Journal}, issn = {0168-9274}, journal = {Appl. Numer. Math.}, mrclass = {65M08}, mrnumber = {2899255}, number = 4, owner = {szur}, pages = {441--456}, title = {Finite volume schemes for hyperbolic balance laws with multiplicative noise}, url = {http://dx.doi.org/10.1016/j.apnum.2011.01.011}, volume = 62, year = 2012 }
7. C. Rohde and F. Xie, “Global existence and blowup phenomenon for a 1D radiation hydrodynamics model problem,” Math. Methods Appl. Sci., vol. 35, no. 5, pp. 564--573, 2012.
  - BibTeX
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  @article{rohde2012global, author = {Rohde, Christian and Xie, Feng}, doi = {10.1002/mma.1593}, fjournal = {Mathematical Methods in the Applied Sciences}, issn = {0170-4214}, journal = {Math. Methods Appl. Sci.}, mrclass = {35Q35 (35A09 35B44 76X05)}, mrnumber = {2908767}, number = 5, owner = {szur}, pages = {564--573}, title = {Global existence and blowup phenomenon for a 1{D} radiation hydrodynamics model problem}, url = {http://dx.doi.org/10.1002/mma.1593}, volume = 35, year = 2012 }
8. C. Chalons, F. Coquel, P. Engel, and C. Rohde, “Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems,” SIAM Journal on Scientific Computing, vol. 34, no. 3, pp. A1753--A1776, 2012.
  - BibTeX
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  @article{chalons2012relaxation, author = {Chalons, C. and Coquel, F. and Engel, P. and Rohde, C.}, doi = {10.1137/110848815}, eprint = {http://epubs.siam.org/doi/pdf/10.1137/110848815}, journal = {SIAM Journal on Scientific Computing}, number = 3, pages = {A1753--A1776}, title = {Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems}, url = {http://epubs.siam.org/doi/abs/10.1137/110848815}, volume = 34, year = 2012 }
9. F. Kissling, R. Helmig, and C. Rohde, “Simulation of Infiltration Processes in the Unsaturated Zone Using a Multi-Scale Approach,” Vadose Zone J., vol. 11, no. 3, p. , 2012.
  - BibTeX
  - Link
  @article{kissling2012simulation, author = {Kissling, F. and Helmig, R. and Rohde, C.}, doi = {10.2136/vzj2011.0193}, journal = {Vadose Zone J.}, number = 3, owner = {kissling}, pages = {-}, title = {{S}imulation of {I}nfiltration {P}rocesses in the {U}nsaturated {Z}one {U}sing a {M}ulti-{S}cale {A}pproach}, url = {http://dx.doi.org/10.2136/vzj2011.0193}, volume = 11, year = 2012 }
2011
1. R. Bürger, I. Kröker, and C. Rohde, “Uncertainty quantification for a clarifier-thickener model with random feed,” in Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2, vol. 4, Springer, 2011, pp. 195--203.
  - BibTeX
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  @incollection{burger2011uncertainty, author = {Bürger, Raimund and Kröker, Ilja and Rohde, Christian}, booktitle = {Finite volumes for complex applications. VI. Problems \& perspectives. Volume 1, 2}, doi = {10.1007/978-3-642-20671-9_21}, owner = {seusdd}, pages = {195--203}, publisher = {Springer}, title = {Uncertainty quantification for a clarifier-thickener model with random feed}, url = {http://dx.doi.org/10.1007/978-3-642-20671-9_21}, volume = 4, year = 2011 }
2010
1. F. Kissling and C. Rohde, “The Computation of Nonclassical Shock Waves with a Heterogeneous Multiscale Method,” Netw. Heterog. Media, vol. 5, no. 3, pp. 661--674, 2010.
  - BibTeX
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  @article{kissling2010computation, author = {Kissling, Frederike and Rohde, Christian}, doi = {10.3934/nhm.2010.5.661}, fjournal = {Networks and Heterogeneous Media}, issn = {1556-1801}, journal = {Netw. Heterog. Media}, mrclass = {65M50 (35L65 65M99 76L05 76N15 76S05)}, mrnumber = {2670661 (2011j:65204)}, mrreviewer = {Long An Ying}, number = 3, pages = {661--674}, title = {The {C}omputation of {N}onclassical {S}hock {W}aves with a {H}eterogeneous {M}ultiscale {M}ethod}, url = {http://dx.doi.org/10.3934/nhm.2010.5.661}, volume = 5, year = 2010 }
2. C. Rohde, “A local and low-order Navier-Stokes-Korteweg system,” in Nonlinear partial differential equations and hyperbolic wave phenomena, vol. 526, Providence, RI: Amer. Math. Soc., 2010, pp. 315--337.
  - BibTeX
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  @incollection{rohde2010local, address = {Providence, RI}, author = {Rohde, Christian}, booktitle = {Nonlinear partial differential equations and hyperbolic wave phenomena}, doi = {10.1090/conm/526/10387}, mrclass = {35Q30 (35Q53 76N10)}, mrnumber = {2731998 (2012c:35331)}, mrreviewer = {Rapha{\"e}l Danchin}, owner = {szur}, pages = {315--337}, publisher = {Amer. Math. Soc.}, series = {Contemp. Math.}, title = {A local and low-order {N}avier-{S}tokes-{K}orteweg system}, url = {http://dx.doi.org/10.1090/conm/526/10387}, volume = 526, year = 2010 }
2009
1. F. Kissling, P. G. LeFloch, and C. Rohde, “A Kinetic Decomposition for Singular Limits of non-local Conservation Laws,” J. Differential Equations, vol. 247, no. 12, pp. 3338--3356, 2009.
  - BibTeX
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  @article{kissling2009kinetic, author = {Kissling, Frederike and LeFloch, Philippe G. and Rohde, Christian}, coden = {JDEQAK}, doi = {10.1016/j.jde.2009.05.006}, fjournal = {Journal of Differential Equations}, issn = {0022-0396}, journal = {J. Differential Equations}, mrclass = {35L65}, mrnumber = {2571580 (2011a:35334)}, mrreviewer = {Konstantina Trivisa}, number = 12, owner = {szur}, pages = {3338--3356}, title = {{A} {K}inetic {D}ecomposition for {S}ingular {L}imits of non-local {C}onservation {L}aws}, url = {http://dx.doi.org/10.1016/j.jde.2009.05.006}, volume = 247, year = 2009 }
2008
1. C. Rohde, N. Tiemann, and W.-A. Yong, “Weak and classical solutions for a model problem in radiation hydrodynamics,” in Hyperbolic problems: theory, numerics, applications, Berlin: Springer, 2008, pp. 891--899.
  - BibTeX
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  @incollection{rohde2008classical, address = {Berlin}, author = {Rohde, C. and Tiemann, N. and Yong, W.-A.}, booktitle = {Hyperbolic problems: theory, numerics, applications}, doi = {10.1007/978-3-540-75712-2_93}, mrclass = {76W05 (35A01 35D30 35Q35)}, mrnumber = {2549228}, owner = {szur}, pages = {891--899}, publisher = {Springer}, title = {Weak and classical solutions for a model problem in radiation hydrodynamics}, url = {http://dx.doi.org/10.1007/978-3-540-75712-2_93}, year = 2008 }
2. C. Rohde and W.-A. Yong, “Dissipative entropy and global smooth solutions in radiation hydrodynamics and magnetohydrodynamics,” Math. Models Methods Appl. Sci., vol. 18, no. 12, pp. 2151--2174, 2008.
  - BibTeX
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  @article{rohde2008dissipative, author = {Rohde, Christian and Yong, Wen-An}, doi = {10.1142/S0218202508003327}, fjournal = {Mathematical Models \& Methods in Applied Sciences}, issn = {0218-2025}, journal = {Math. Models Methods Appl. Sci.}, mrclass = {76W05 (35Q35)}, mrnumber = {2477720 (2010a:76094)}, mrreviewer = {Omar Maj}, number = 12, owner = {szur}, pages = {2151--2174}, title = {Dissipative entropy and global smooth solutions in radiation hydrodynamics and magnetohydrodynamics}, url = {http://dx.doi.org/10.1142/S0218202508003327}, volume = 18, year = 2008 }
3. A. Dressel and C. Rohde, “A finite-volume approach to liquid-vapour fluids with phase transition,” in Finite volumes for complex applications V, ISTE, London, 2008, pp. 53--68.
  - BibTeX
  @incollection{dressel2008finitevolume, author = {Dressel, Alexander and Rohde, Christian}, booktitle = {Finite volumes for complex applications {V}}, mrclass = {76M12 (65M06 76T10 80A22)}, mrnumber = {2441446 (2009j:76163)}, mrreviewer = {Jakub Siemek}, owner = {szur}, pages = {53--68}, publisher = {ISTE, London}, title = {A finite-volume approach to liquid-vapour fluids with phase transition}, year = 2008 }
4. J. Haink and C. Rohde, “Local discontinuous-Galerkin schemes for model problems in phase transition theory,” Commun. Comput. Phys., vol. 4, pp. 860–893, 2008.
  - BibTeX
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  @article{haink2008local, author = {Haink, J. and Rohde, C.}, journal = {Commun. Comput. Phys.}, owner = {joosde}, pages = {860-893}, title = {Local discontinuous-{G}alerkin schemes for model problems in phase transition theory}, url = {https://www.researchgate.net/profile/Christian_Rohde2/publication/228406932_Local_discontinuous-Galerkin_schemes_for_model_problems_in_phase_transition_theory/links/00b4952cb030e0da90000000.pdf}, volume = 4, year = 2008 }
5. A. Dressel and C. Rohde, “Global existence and uniqueness of solutions for a viscoelastic two-phase model,” Indiana Univ. Math. J., vol. 57, no. 2, pp. 717--755, 2008.
  - BibTeX
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  @article{dressel2008global, author = {Dressel, Alexander and Rohde, Christian}, coden = {IUMJAB}, doi = {10.1512/iumj.2008.57.3271}, fjournal = {Indiana University Mathematics Journal}, issn = {0022-2518}, journal = {Indiana Univ. Math. J.}, mrclass = {35Q72 (35B30 35D05 74A30 74D10 74H20)}, mrnumber = {2414333 (2009e:35278)}, mrreviewer = {Marcelo M. Cavalcanti}, number = 2, owner = {szur}, pages = {717--755}, title = {Global existence and uniqueness of solutions for a viscoelastic two-phase model}, url = {http://dx.doi.org/10.1512/iumj.2008.57.3271}, volume = 57, year = 2008 }
2007
1. C. Rohde and W.-A. Yong, “The nonrelativistic limit in radiation hydrodynamics. I. Weak entropy solutions for a model problem,” J. Differential Equations, vol. 234, no. 1, pp. 91--109, 2007.
  - BibTeX
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  @article{rohde2007nonrelativistic, author = {Rohde, Christian and Yong, Wen-An}, coden = {JDEQAK}, doi = {10.1016/j.jde.2006.11.010}, fjournal = {Journal of Differential Equations}, issn = {0022-0396}, journal = {J. Differential Equations}, mrclass = {35Q35}, mrnumber = {2298966 (2008c:35256)}, mrreviewer = {Philippe G. LeFloch}, number = 1, owner = {szur}, pages = {91--109}, title = {The nonrelativistic limit in radiation hydrodynamics. {I}. {W}eak entropy solutions for a model problem}, url = {http://dx.doi.org/10.1016/j.jde.2006.11.010}, volume = 234, year = 2007 }
2. C. Merkle and C. Rohde, “The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques,” M2AN Math. Model. Numer. Anal., vol. 41, no. 6, pp. 1089--1123, 2007.
  - BibTeX
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  @article{merkle2007sharpinterface, author = {Merkle, Christian and Rohde, Christian}, doi = {10.1051/m2an:2007048}, fjournal = {M2AN. Mathematical Modelling and Numerical Analysis}, issn = {0764-583X}, journal = {M2AN Math. Model. Numer. Anal.}, mrclass = {76T10 (35L65 35Q35 76M25 80A22)}, mrnumber = {2377108 (2008j:76068)}, mrreviewer = {Denis Serre}, number = 6, owner = {szur}, pages = {1089--1123}, title = {The sharp-interface approach for fluids with phase change: {R}iemann problems and ghost fluid techniques}, url = {http://dx.doi.org/10.1051/m2an:2007048}, volume = 41, year = 2007 }
2006
1. J. Haink and C. Rohde, “Phase transition in compressible media and nonlocal capillarity terms,” in Hyperbolic problems: theory, numerics and applications. I, Yokohama Publ., Yokohama, 2006, pp. 147--154.
  - BibTeX
  @incollection{haink2006phase, author = {Haink, Jenny and Rohde, Christian}, booktitle = {Hyperbolic problems: theory, numerics and applications. {I}}, mrclass = {35Q35 (35C07 76D45)}, mrnumber = {2667232}, owner = {szur}, pages = {147--154}, publisher = {Yokohama Publ., Yokohama}, title = {Phase transition in compressible media and nonlocal capillarity terms}, year = 2006 }
2. D. Diehl and C. Rohde, “On the structure of MHD shock waves in diffusive-dispersive media,” J. Math. Fluid Mech., vol. 8, no. 1, pp. 120--145, 2006.
  - BibTeX
  - Link
  @article{diehl2006structure, author = {Diehl, Dennis and Rohde, Christian}, doi = {10.1007/s00021-004-0149-z}, fjournal = {Journal of Mathematical Fluid Mechanics}, issn = {1422-6928}, journal = {J. Math. Fluid Mech.}, mrclass = {76W05 (35L70 37M20 37N10 76L05)}, mrnumber = {2205154 (2006j:76164)}, mrreviewer = {Dehua Wang}, number = 1, owner = {szur}, pages = {120--145}, title = {On the structure of {MHD} shock waves in diffusive-dispersive media}, url = {http://dx.doi.org/10.1007/s00021-004-0149-z}, volume = 8, year = 2006 }
3. C. Merkle and C. Rohde, “Computation of dynamical phase transitions in solids,” Appl. Numer. Math., vol. 56, no. 10–11, pp. 1450--1463, 2006.
  - BibTeX
  - Link
  @article{merkle2006computation, author = {Merkle, C. and Rohde, C.}, coden = {ANMAEL}, doi = {10.1016/j.apnum.2006.03.025}, fjournal = {Applied Numerical Mathematics. An IMACS Journal}, issn = {0168-9274}, journal = {Appl. Numer. Math.}, mrclass = {74N99 (74H15 74J40 74N15 82C26)}, mrnumber = {2245467 (2007i:74093)}, number = {10-11}, owner = {szur}, pages = {1450--1463}, title = {Computation of dynamical phase transitions in solids}, url = {http://dx.doi.org/10.1016/j.apnum.2006.03.025}, volume = 56, year = 2006 }
4. V. Jovanović and C. Rohde, “Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws,” SIAM J. Numer. Anal., vol. 43, no. 6, pp. 2423--2449 (electronic), 2006.
  - BibTeX
  - Link
  @article{jovanovic2006error, author = {Jovanovi{\'c}, Vladimir and Rohde, Christian}, doi = {10.1137/S0036142903438136}, fjournal = {SIAM Journal on Numerical Analysis}, issn = {0036-1429}, journal = {SIAM J. Numer. Anal.}, mrclass = {65M12 (35L60 35L65 65M06)}, mrnumber = {2206442 (2006j:65263)}, mrreviewer = {Doron Levy}, number = 6, owner = {szur}, pages = {2423--2449 (electronic)}, title = {Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws}, url = {http://dx.doi.org/10.1137/S0036142903438136}, volume = 43, year = 2006 }
2005
1. C. Rohde, “Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms,” SIAM J. Math. Anal., vol. 37, no. 1, pp. 103--129 (electronic), 2005.
  - BibTeX
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  @article{rohde2005scalar, author = {Rohde, Christian}, doi = {10.1137/S0036141004443300}, fjournal = {SIAM Journal on Mathematical Analysis}, issn = {0036-1410}, journal = {SIAM J. Math. Anal.}, mrclass = {35L65 (35L67)}, mrnumber = {2176925 (2006k:35183)}, mrreviewer = {Stefano Bianchini}, number = 1, owner = {szur}, pages = {103--129 (electronic)}, title = {Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms}, url = {http://dx.doi.org/10.1137/S0036141004443300}, volume = 37, year = 2005 }
2. F. Coquel, D. Diehl, C. Merkle, and C. Rohde, “Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows,” in Numerical methods for hyperbolic and kinetic problems, vol. 7, Eur. Math. Soc., Zürich, 2005, pp. 239--270.
  - BibTeX
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  @incollection{coquel2005sharp, author = {Coquel, F. and Diehl, D. and Merkle, C. and Rohde, C.}, booktitle = {Numerical methods for hyperbolic and kinetic problems}, doi = {10.4171/012-1/11}, mrclass = {80A22 (65M06 76N99)}, mrnumber = {2186374 (2006j:80005)}, mrreviewer = {Ulisse Stefanelli}, owner = {szur}, pages = {239--270}, publisher = {Eur. Math. Soc., Z\"urich}, series = {IRMA Lect. Math. Theor. Phys.}, title = {Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows}, url = {http://dx.doi.org/10.4171/012-1/11}, volume = 7, year = 2005 }
3. M. J. Gander and C. Rohde, “Overlapping Schwarz waveform relaxation for convection-dominated nonlinear conservation laws,” SIAM J. Sci. Comput., vol. 27, no. 2, pp. 415--439, 2005.
  - BibTeX
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  @article{gander2005overlapping, author = {Gander, Martin J. and Rohde, Christian}, doi = {10.1137/030601090}, fjournal = {SIAM Journal on Scientific Computing}, issn = {1064-8275}, journal = {SIAM J. Sci. Comput.}, mrclass = {35L65 (35B25 35K55 65M55)}, mrnumber = {2202227 (2006i:35234)}, number = 2, owner = {szur}, pages = {415--439}, title = {Overlapping {S}chwarz waveform relaxation for convection-dominated nonlinear conservation laws}, url = {http://dx.doi.org/10.1137/030601090}, volume = 27, year = 2005 }
4. V. Jovanović and C. Rohde, “Finite-volume schemes for Friedrichs systems in multiple space dimensions: a priori and a posteriori error estimates,” Numer. Methods Partial Differential Equations, vol. 21, no. 1, pp. 104--131, 2005.
  - BibTeX
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  @article{jovanovic2005finitevolume, author = {Jovanovi{\'c}, Vladimir and Rohde, Christian}, doi = {10.1002/num.20026}, fjournal = {Numerical Methods for Partial Differential Equations. An International Journal}, issn = {0749-159X}, journal = {Numer. Methods Partial Differential Equations}, mrclass = {65M06 (35L45 65M15)}, mrnumber = {2100303 (2005h:65134)}, number = 1, owner = {szur}, pages = {104--131}, title = {Finite-volume schemes for {F}riedrichs systems in multiple space dimensions: a priori and a posteriori error estimates}, url = {http://dx.doi.org/10.1002/num.20026}, volume = 21, year = 2005 }
5. C. Rohde, “On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour phase transitions,” ZAMM Z. Angew. Math. Mech., vol. 85, no. 12, pp. 839--857, 2005.
  - BibTeX
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  @article{rohde2005local, author = {Rohde, Christian}, doi = {10.1002/zamm.200410211}, fjournal = {ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics}, issn = {0044-2267}, journal = {ZAMM Z. Angew. Math. Mech.}, mrclass = {35Q35 (35B30 76N10 76T10 80A22)}, mrnumber = {2184845 (2006h:35217)}, number = 12, owner = {szur}, pages = {839--857}, title = {On local and non-local {N}avier-{S}tokes-{K}orteweg systems for liquid-vapour phase transitions}, url = {http://dx.doi.org/10.1002/zamm.200410211}, volume = 85, year = 2005 }
6. C. Rohde, “Phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy,” Interfaces Free Bound., vol. 7, no. 1, pp. 107--129, 2005.
  - BibTeX
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  @article{rohde2005phase, author = {Rohde, Christian}, doi = {10.4171/IFB/116}, fjournal = {Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation}, issn = {1463-9963}, journal = {Interfaces Free Bound.}, mrclass = {35L65 (35L45 35L67 35Q72 74N99 82B26)}, mrnumber = {2126146 (2005k:35268)}, mrreviewer = {Nicole Turb{\'e}}, number = 1, owner = {szur}, pages = {107--129}, title = {Phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy}, url = {http://dx.doi.org/10.4171/IFB/116}, volume = 7, year = 2005 }
7. M. J. Gander and C. Rohde, “Nonlinear advection problems and overlapping Schwarz waveform relaxation,” in Domain decomposition methods in science and engineering, vol. 40, Berlin: Springer, 2005, pp. 251--258.
  - BibTeX
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  @incollection{gander2005nonlinear, address = {Berlin}, author = {Gander, Martin J. and Rohde, Christian}, booktitle = {Domain decomposition methods in science and engineering}, doi = {10.1007/3-540-26825-1_23}, mrclass = {65M55}, mrnumber = {2235749}, owner = {szur}, pages = {251--258}, publisher = {Springer}, series = {Lect. Notes Comput. Sci. Eng.}, title = {Nonlinear advection problems and overlapping {S}chwarz waveform relaxation}, url = {http://dx.doi.org/10.1007/3-540-26825-1_23}, volume = 40, year = 2005 }
8. A. Dedner, D. Kröner, C. Rohde, and M. Wesenberg, “Radiation magnetohydrodynamics: analysis for model problems and efficient 3d-simulations for the full system,” in Analysis and numerics for conservation laws, Berlin: Springer, 2005, pp. 163--202.
  - BibTeX
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  @incollection{dedner2005radiation, address = {Berlin}, author = {Dedner, A. and Kr{\"o}ner, D. and Rohde, C. and Wesenberg, M.}, booktitle = {Analysis and numerics for conservation laws}, doi = {10.1007/3-540-27907-5_8}, mrclass = {85A30 (35B35 35Q35 76W05 85-08)}, mrnumber = {2169928 (2006m:85002)}, mrreviewer = {Nina G. Khatiashvili}, owner = {szur}, pages = {163--202}, publisher = {Springer}, title = {Radiation magnetohydrodynamics: analysis for model problems and efficient 3d-simulations for the full system}, url = {http://dx.doi.org/10.1007/3-540-27907-5_8}, year = 2005 }
2004
1. A. Dedner, C. Rohde, B. Schupp, and M. Wesenberg, “A parallel, load-balanced MHD code on locally-adapted unstructured grids in 3d,” Comput. Vis. Sci., vol. 7, no. 2, pp. 79--96, 2004.
  - BibTeX
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  @article{dedner2004parallel, author = {Dedner, Andreas and Rohde, Christian and Schupp, Bernhard and Wesenberg, Matthias}, doi = {10.1007/s00791-004-0140-5}, fjournal = {Computing and Visualization in Science}, issn = {1432-9360}, journal = {Comput. Vis. Sci.}, mrclass = {76M12 (65M50 76W05 85A30)}, mrnumber = {2088784 (2006a:76075)}, mrreviewer = {Alexander M. Blokhin}, number = 2, owner = {szur}, pages = {79--96}, title = {A parallel, load-balanced {MHD} code on locally-adapted unstructured grids in 3d}, url = {http://dx.doi.org/10.1007/s00791-004-0140-5}, volume = 7, year = 2004 }
2. A. Dedner and C. Rohde, “Numerical approximation of entropy solutions for hyperbolic integro-differential equations,” Numer. Math., vol. 97, no. 3, pp. 441--471, 2004.
  - BibTeX
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  @article{dedner2004numerical, author = {Dedner, Andreas and Rohde, Christian}, coden = {NUMMA7}, doi = {10.1007/s00211-003-0502-9}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {45K05 (35L60 35Q35 65M06 65M15)}, mrnumber = {2059465 (2005f:45016)}, mrreviewer = {Guillaume Bal}, number = 3, owner = {szur}, pages = {441--471}, title = {Numerical approximation of entropy solutions for hyperbolic integro-differential equations}, url = {http://dx.doi.org/10.1007/s00211-003-0502-9}, volume = 97, year = 2004 }
3. C. Rohde and M. D. Thanh, “Global existence for phase transition problems via a variational scheme,” J. Hyperbolic Differ. Equ., vol. 1, no. 4, pp. 747--768, 2004.
  - BibTeX
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  @article{rohde2004global, author = {Rohde, Christian and Thanh, Mai Duc}, doi = {10.1142/S0219891604000329}, fjournal = {Journal of Hyperbolic Differential Equations}, issn = {0219-8916}, journal = {J. Hyperbolic Differ. Equ.}, mrclass = {35K50 (35A35 74H20 74N99)}, mrnumber = {2111581 (2005k:35183)}, mrreviewer = {L. Hsiao}, number = 4, owner = {szur}, pages = {747--768}, title = {Global existence for phase transition problems via a variational scheme}, url = {http://dx.doi.org/10.1142/S0219891604000329}, volume = 1, year = 2004 }
2003
1. D. Kröner, M. Küther, M. Ohlberger, and C. Rohde, “A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws,” in Trends in nonlinear analysis, Berlin: Springer, 2003, pp. 289--306.
  - BibTeX
  @incollection{kroner2003posteriori, address = {Berlin}, author = {Kr{\"o}ner, Dietmar and K{\"u}ther, Marc and Ohlberger, Mario and Rohde, Christian}, booktitle = {Trends in nonlinear analysis}, mrclass = {65M15 (65M06 65M50 76M12)}, mrnumber = {1999102 (2004g:65117)}, owner = {szur}, pages = {289--306}, publisher = {Springer}, title = {A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws}, year = 2003 }
2. A. Dedner, D. Kröner, C. Rohde, T. Schnitzer, and M. Wesenberg, “Comparison of finite volume and discontinuous Galerkin methods of higher order for systems of conservation laws in multiple space dimensions,” in Geometric analysis and nonlinear partial differential equations, Berlin: Springer, 2003, pp. 573--589.
  - BibTeX
  @incollection{dedner2003comparison, address = {Berlin}, author = {Dedner, A. and Kr{\"o}ner, D. and Rohde, C. and Schnitzer, T. and Wesenberg, M.}, booktitle = {Geometric analysis and nonlinear partial differential equations}, mrclass = {65M06 (35L65 65M60 76M10 76M12)}, mrnumber = {2008357}, owner = {szur}, pages = {573--589}, publisher = {Springer}, title = {Comparison of finite volume and discontinuous {G}alerkin methods of higher order for systems of conservation laws in multiple space dimensions}, year = 2003 }
3. C. Rohde and W. Zajaczkowski, “On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation,” Appl. Math., vol. 48, no. 4, pp. 257--277, 2003.
  - BibTeX
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  @article{rohde2003cauchy, author = {Rohde, C. and Zaj{\polhk{a}}czkowski, W.}, doi = {10.1023/A:1026010631074}, fjournal = {Applications of Mathematics}, issn = {0862-7940}, journal = {Appl. Math.}, mrclass = {35Q35 (35L60 35Q60 76N10 76W05)}, mrnumber = {1994377 (2004f:35147)}, mrreviewer = {Paolo Secchi}, number = 4, owner = {szur}, pages = {257--277}, title = {On the {C}auchy problem for the equations of ideal compressible {MHD} fluids with radiation}, url = {http://dx.doi.org/10.1023/A:1026010631074}, volume = 48, year = 2003 }
4. A. Dedner, C. Rohde, and M. Wesenberg, “Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics,” in Hyperbolic problems: theory, numerics, applications, Berlin: Springer, 2003, pp. 499--508.
  - BibTeX
  @incollection{dedner2003efficient, address = {Berlin}, author = {Dedner, Andreas and Rohde, Christian and Wesenberg, Matthias}, booktitle = {Hyperbolic problems: theory, numerics, applications}, mrclass = {65M06 (35Q35 65M50 76M12)}, mrnumber = {2053199}, owner = {szur}, pages = {499--508}, publisher = {Springer}, title = {Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics}, year = 2003 }
5. A. Dedner, C. Rohde, and M. Wesenberg, “A new approach to divergence cleaning in magnetohydrodynamic simulations,” in Hyperbolic problems: theory, numerics, applications, Berlin: Springer, 2003, pp. 509--518.
  - BibTeX
  @incollection{dedner2003approach, address = {Berlin}, author = {Dedner, Andreas and Rohde, Christian and Wesenberg, Matthias}, booktitle = {Hyperbolic problems: theory, numerics, applications}, mrclass = {76M25 (76W05)}, mrnumber = {2053200}, owner = {szur}, pages = {509--518}, publisher = {Springer}, title = {A new approach to divergence cleaning in magnetohydrodynamic simulations}, year = 2003 }
6. H. Freistühler and C. Rohde, “The bifurcation analysis of the MHD Rankine-Hugoniot equations for a perfect gas,” Phys. D, vol. 185, no. 2, pp. 78--96, 2003.
  - BibTeX
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  @article{freistuhler2003bifurcation, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, coden = {PDNPDT}, doi = {10.1016/S0167-2789(03)00206-9}, fjournal = {Physica D. Nonlinear Phenomena}, issn = {0167-2789}, journal = {Phys. D}, mrclass = {76L05 (35B32 35L67 76N15 76W05)}, mrnumber = {2014893 (2004k:76079)}, mrreviewer = {Alastair M. Rucklidge}, number = 2, owner = {szur}, pages = {78--96}, title = {The bifurcation analysis of the {MHD} {R}ankine-{H}ugoniot equations for a perfect gas}, url = {http://dx.doi.org/10.1016/S0167-2789(03)00206-9}, volume = 185, year = 2003 }
2002
1. A. Dedner and C. Rohde, “FV-schemes for a scalar model problem of radiation magnetohydrodynamics,” in Finite volumes for complex applications, III (Porquerolles, 2002), Hermes Sci. Publ., Paris, 2002, pp. 165--172.
  - BibTeX
  @incollection{dedner2002fvschemes, author = {Dedner, Andreas and Rohde, Christian}, booktitle = {Finite volumes for complex applications, {III} ({P}orquerolles, 2002)}, mrclass = {65M06 (76W05 78A40 85A30)}, mrnumber = {2007414}, owner = {szur}, pages = {165--172}, publisher = {Hermes Sci. Publ., Paris}, title = {F{V}-schemes for a scalar model problem of radiation magnetohydrodynamics}, year = 2002 }
2. H. Freistühler and C. Rohde, “Numerical computation of viscous profiles for hyperbolic conservation laws,” Math. Comp., vol. 71, no. 239, pp. 1021--1042 (electronic), 2002.
  - BibTeX
  - Link
  @article{freistuhler2002numerical, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, coden = {MCMPAF}, doi = {10.1090/S0025-5718-01-01340-0}, fjournal = {Mathematics of Computation}, issn = {0025-5718}, journal = {Math. Comp.}, mrclass = {65M99 (35L65 76M25 76N10 76W05)}, mrnumber = {1898744 (2003f:65178)}, mrreviewer = {Gholam-Ali Zakeri}, number = 239, owner = {szur}, pages = {1021--1042 (electronic)}, title = {Numerical computation of viscous profiles for hyperbolic conservation laws}, url = {http://dx.doi.org/10.1090/S0025-5718-01-01340-0}, volume = 71, year = 2002 }
3. M. Ohlberger and C. Rohde, “Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems,” IMA J. Numer. Anal., vol. 22, no. 2, pp. 253--280, 2002.
  - BibTeX
  - Link
  @article{ohlberger2002adaptive, author = {Ohlberger, Mario and Rohde, Christian}, coden = {IJNADN}, doi = {10.1093/imanum/22.2.253}, fjournal = {IMA Journal of Numerical Analysis}, issn = {0272-4979}, journal = {IMA J. Numer. Anal.}, mrclass = {65M06 (65M15 76M12)}, mrnumber = {1897409 (2003e:65152)}, number = 2, owner = {szur}, pages = {253--280}, title = {Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems}, url = {http://dx.doi.org/10.1093/imanum/22.2.253}, volume = 22, year = 2002 }
4. P. G. Lefloch, J. M. Mercier, and C. Rohde, “Fully discrete, entropy conservative schemes of arbitrary order,” SIAM J. Numer. Anal., vol. 40, no. 5, pp. 1968--1992 (electronic), 2002.
  - BibTeX
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  @article{lefloch2002fully, author = {Lefloch, P. G. and Mercier, J. M. and Rohde, C.}, doi = {10.1137/S003614290240069X}, fjournal = {SIAM Journal on Numerical Analysis}, issn = {0036-1429}, journal = {SIAM J. Numer. Anal.}, mrclass = {65M06 (35L65 35M10)}, mrnumber = {1950629 (2003k:65088)}, mrreviewer = {Dennis C. Jespersen}, number = 5, owner = {szur}, pages = {1968--1992 (electronic)}, title = {Fully discrete, entropy conservative schemes of arbitrary order}, url = {http://dx.doi.org/10.1137/S003614290240069X}, volume = 40, year = 2002 }
2001
1. B. Haasdonk, D. Kr�ner, and C. Rohde, “Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids,” Numer. Math., vol. 88, no. 3, pp. 459--484, 2001.
  - BibTeX
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kr�ner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:/afs/.mathe/public/www/ians/am/Haasdonk/publications/HKR01.pdf:PDF}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M06}, mrnumber = {1835467 (2002c:65133)}, mrreviewer = {Kenneth H. Karlsen}, number = 3, owner = {szur}, pages = {459--484}, title = {Convergence of a staggered {L}ax-{F}riedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids}, volume = 88, year = 2001 }
2. H. Freistühler, C. Fries, and C. Rohde, “Existence, bifurcation, and stability of profiles for classical and non-classical shock waves,” in Ergodic theory, analysis, and efficient simulation of dynamical systems, Berlin: Springer, 2001, pp. 287--309, 814.
  - BibTeX
  @incollection{freistuhler2001existence, address = {Berlin}, author = {Freist{\"u}hler, Heinrich and Fries, Christian and Rohde, Christian}, booktitle = {Ergodic theory, analysis, and efficient simulation of dynamical systems}, mrclass = {35L67 (35B35 35L65 35Q35 76L05 76W05)}, mrnumber = {1850311 (2002g:35150)}, mrreviewer = {Kenji Nishihara}, owner = {szur}, pages = {287--309, 814}, publisher = {Springer}, title = {Existence, bifurcation, and stability of profiles for classical and non-classical shock waves}, year = 2001 }
3. A. Dedner, D. Kröner, C. Rohde, and M. Wesenberg, “Godunov-type schemes for the MHD equations,” in Godunov methods (Oxford, 1999), Kluwer/Plenum, New York, 2001, pp. 209--216.
  - BibTeX
  @incollection{dedner2001godunovtype, author = {Dedner, A. and Kr{\"o}ner, D. and Rohde, C. and Wesenberg, M.}, booktitle = {Godunov methods ({O}xford, 1999)}, mrclass = {76M20 (76W05)}, mrnumber = {1963594}, owner = {szur}, pages = {209--216}, publisher = {Kluwer/Plenum, New York}, title = {Godunov-type schemes for the {MHD} equations}, year = 2001 }
4. H. Freistühler and C. Rohde, “A numerical study on viscous profiles of MHD shock waves,” in Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000), vol. 141, Basel: Birkhäuser, 2001, pp. 399--408.
  - BibTeX
  @incollection{freistuhler2001numerical, address = {Basel}, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, booktitle = {Hyperbolic problems: theory, numerics, applications, {V}ol. {I}, {II} ({M}agdeburg, 2000)}, mrclass = {76M25 (35Q35 76L05 76W05)}, mrnumber = {1882941}, owner = {szur}, pages = {399--408}, publisher = {Birkh\"auser}, series = {Internat. Ser. Numer. Math., 140}, title = {A numerical study on viscous profiles of {MHD} shock waves}, volume = 141, year = 2001 }
5. P. G. LeFloch and C. Rohde, “Zero diffusion-dispersion limits for self-similar Riemann solutions to hyperbolic systems of conservation laws,” Indiana Univ. Math. J., vol. 50, no. 4, pp. 1707--1743, 2001.
  - BibTeX
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  @article{lefloch2001diffusiondispersion, author = {LeFloch, Philippe G. and Rohde, Christian}, coden = {IUMJAB}, doi = {10.1512/iumj.2001.50.2057}, fjournal = {Indiana University Mathematics Journal}, issn = {0022-2518}, journal = {Indiana Univ. Math. J.}, mrclass = {35L65}, mrnumber = {1889079 (2002k:35194)}, mrreviewer = {Denis Serre}, number = 4, owner = {szur}, pages = {1707--1743}, title = {Zero diffusion-dispersion limits for self-similar {R}iemann solutions to hyperbolic systems of conservation laws}, url = {http://dx.doi.org/10.1512/iumj.2001.50.2057}, volume = 50, year = 2001 }
6. T. Hillen, C. Rohde, and F. Lutscher, “Existence of weak solutions for a hyperbolic model of chemosensitive movement,” J. Math. Anal. Appl., vol. 260, no. 1, pp. 173--199, 2001.
  - BibTeX
  - Link
  @article{hillen2001existence, author = {Hillen, Thomas and Rohde, Christian and Lutscher, Frithjof}, coden = {JMANAK}, doi = {10.1006/jmaa.2001.7447}, fjournal = {Journal of Mathematical Analysis and Applications}, issn = {0022-247X}, journal = {J. Math. Anal. Appl.}, mrclass = {35Q80 (35A35 35D05 35L60 92C17)}, mrnumber = {1843975 (2003c:35153)}, number = 1, owner = {szur}, pages = {173--199}, title = {Existence of weak solutions for a hyperbolic model of chemosensitive movement}, url = {http://dx.doi.org/10.1006/jmaa.2001.7447}, volume = 260, year = 2001 }
7. B. Haasdonk, D. Kröner, and C. Rohde, “Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids,” Numer. Math., vol. 88, no. 3, pp. 459--484, 2001.
  - BibTeX
  - Link
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kr{\"o}ner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2001a_www_preprint_StgLxF_convergence.pdf:PDF}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M06}, mrnumber = {MR1835467 (2002c:65133)}, mrreviewer = {Kenneth H. Karlsen}, number = 3, owner = {haasdonk}, pages = {459--484}, title = {Convergence of a staggered {L}ax-{F}riedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids}, url = {http://dx.doi.org/10.1007/s211-001-8011-x}, volume = 88, year = 2001 }
8. A. Dedner, D. Kröner, C. Rohde, and M. Wesenberg, “MHD instabilities arising in solar physics: a numerical approach,” in Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000), vol. 141, Basel: Birkhäuser, 2001, pp. 277--286.
  - BibTeX
  @incollection{dedner2001instabilities, address = {Basel}, author = {Dedner, Andreas and Kr{\"o}ner, Dietmar and Rohde, Christian and Wesenberg, Matthias}, booktitle = {Hyperbolic problems: theory, numerics, applications, {V}ol. {I}, {II} ({M}agdeburg, 2000)}, mrclass = {85A30 (76E25 76W05 85-08)}, mrnumber = {1882928}, owner = {szur}, pages = {277--286}, publisher = {Birkh\"auser}, series = {Internat. Ser. Numer. Math., 140}, title = {M{HD} instabilities arising in solar physics: a numerical approach}, volume = 141, year = 2001 }
2000
1. P. G. Lefloch and C. Rohde, “High-order schemes, entropy inequalities, and nonclassical shocks,” SIAM J. Numer. Anal., vol. 37, no. 6, pp. 2023--2060 (electronic), 2000.
  - BibTeX
  - Link
  @article{lefloch2000highorder, author = {Lefloch, Philippe G. and Rohde, Christian}, doi = {10.1137/S0036142998345256}, fjournal = {SIAM Journal on Numerical Analysis}, issn = {0036-1429}, journal = {SIAM J. Numer. Anal.}, mrclass = {65M12 (35L67 76L05 76M20)}, mrnumber = {1766858 (2001e:65139)}, mrreviewer = {Eun-Jae Park}, number = 6, owner = {szur}, pages = {2023--2060 (electronic)}, title = {High-order schemes, entropy inequalities, and nonclassical shocks}, url = {http://dx.doi.org/10.1137/S0036142998345256}, volume = 37, year = 2000 }
1999
1. A. Dedner, C. Rohde, and M. Wesenberg, “A MHD-simulation in solar physics,” in Finite volumes for complex applications II, Hermes Sci. Publ., Paris, 1999, pp. 491--498.
  - BibTeX
  @incollection{dedner1999mhdsimulation, author = {Dedner, A. and Rohde, C. and Wesenberg, M.}, booktitle = {Finite volumes for complex applications {II}}, mrclass = {65M50 (76W05 85A30)}, mrnumber = {2062167}, owner = {szur}, pages = {491--498}, publisher = {Hermes Sci. Publ., Paris}, title = {A {MHD}-simulation in solar physics}, year = 1999 }
2. H. Freistühler and C. Rohde, “Numerical methods for viscous profiles of non-classical shock waves,” in Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich, 1998), vol. 129, Basel: Birkhäuser, 1999, pp. 333--342.
  - BibTeX
  @incollection{freistuhler1999numerical, address = {Basel}, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, booktitle = {Hyperbolic problems: theory, numerics, applications, {V}ol. {I} ({Z}\"urich, 1998)}, mrclass = {65M30 (76L05 76M25 76W05)}, mrnumber = {1717203 (2000i:65140)}, mrreviewer = {Shi Jin}, owner = {szur}, pages = {333--342}, publisher = {Birkh\"auser}, series = {Internat. Ser. Numer. Math.}, title = {Numerical methods for viscous profiles of non-classical shock waves}, volume = 129, year = 1999 }
1998
1. C. Rohde, “Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D,” Numer. Math., vol. 81, no. 1, pp. 85--123, 1998.
  - BibTeX
  - Link
  @article{rohde1998upwind, author = {Rohde, Christian}, coden = {NUMMA7}, doi = {10.1007/s002110050385}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M60 (35L65 76M25 76N15)}, mrnumber = {1657726 (99j:65174)}, mrreviewer = {Riccardo Fazio}, number = 1, owner = {szur}, pages = {85--123}, title = {Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2{D}}, url = {http://dx.doi.org/10.1007/s002110050385}, volume = 81, year = 1998 }
2. C. Rohde, “Entropy solutions for weakly coupled hyperbolic systems in several space dimensions,” Z. Angew. Math. Phys., vol. 49, no. 3, pp. 470--499, 1998.
  - BibTeX
  - Link
  @article{rohde1998entropy, author = {Rohde, Christian}, coden = {AZMPA8}, doi = {10.1007/s000000050102}, fjournal = {Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physique Appliqu\'ees}, issn = {0044-2275}, journal = {Z. Angew. Math. Phys.}, mrclass = {35L60 (35L65)}, mrnumber = {1629553 (99e:35133)}, mrreviewer = {Ivan Stra{\v{s}}kraba}, number = 3, owner = {szur}, pages = {470--499}, title = {Entropy solutions for weakly coupled hyperbolic systems in several space dimensions}, url = {http://dx.doi.org/10.1007/s000000050102}, volume = 49, year = 1998 }

Teaching

Summer term 2019: Numerische Grundlagen
Winter term 2018/19: Partielle Differentialgleichungen
Summer term 2018: Numerische Mathematik 2

Christian Rohde

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2018

2017

2016

2015

2014

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2010

2009

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2005

2004

2003

2002

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1999

1998

Teaching