This image shows Christian Rohde

Christian Rohde

Prof. Dr.

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

Contact

+49 711 685 65524
 +4971168565599

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.131

Office Hours

Fridays 1:30 - 2:30 pm and by appointment

  1. 2023

    1. M. J. Gander, S. B. Lunowa, and C. Rohde, “Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations,” SIAM J. Sci. Comput., vol. 45, no. 1, Art. no. 1, 2023, doi: 10.1137/21M1415005.
    2. T. Mel’nyk and C. Rohde, “Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks,” arXiv e-prints, 2023. [Online]. Available: https://doi.org/10.48550/arXiv.2302.10105
    3. S. Burbulla, M. Hörl, and C. Rohde, “Flow in Porous Media with Fractures of Varying Aperture,” Accepted by SIAM J. Sci. Comput, 2023, [Online]. Available: https://doi.org/10.48550/arXiv.2207.09301
    4. D. Seus, F. A. Radu, and C. Rohde, “Towards hybrid two-phase modelling using linear domain decomposition,” Numer. Methods Partial Differential Equations, vol. 39, no. 1, Art. no. 1, 2023, doi: https://doi.org/10.1002/num.22906.
    5. J. Keim, A. Schwarz, S. Chiocchetti, C. Rohde, and A. Beck, “A Reinforcement Learning Based Slope Limiter for Two-Dimensional Finite Volume Schemes,” 2023, doi: 10.13140/RG.2.2.18046.87363.
    6. Y. Miao, C. Rohde, and H. Tang, “Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities,” accepted by Stoch. Partial Differ. Equ. Anal. Comput., 2023, [Online]. Available: https://arxiv.org/abs/2105.08607
    7. J. Keim, C.-D. Munz, and C. Rohde, “A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in Confined Domains,” J. Comput. Phys., vol. 474, p. 111830, 2023, doi: https://doi.org/10.1016/j.jcp.2022.111830.
    8. J. Magiera and C. Rohde, “A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate,” submitted, 2023.
    9. S. Burbulla, L. Formaggia, C. Rohde, and A. Scotti, “Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models,” Comput. Methods Appl. Mech. Engrg., vol. 403, 2023, doi: https://doi.org/10.1016/j.cma.2022.115699.
    10. M. J. Gander, S. B. Lunowa, and C. Rohde, “Consistent and Asymptotic-Preserving Finite-Volume Robin Transmission Conditions for Singularly Perturbed Elliptic Equations,” in Domain Decomposition Methods in Science and Engineering XXVI, S. C. Brenner, E. Chung, A. Klawonn, F. Kwok, J. Xu, and J. Zou, Eds., in Domain Decomposition Methods in Science and Engineering XXVI. Cham: Springer International Publishing, 2023, pp. 443--450.

  2. 2022

    1. J. Magiera and C. Rohde, “A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces,” J. Comput. Phys., p. 111551, 2022, doi: https://doi.org/10.1016/j.jcp.2022.111551.
    2. S. Burbulla, A. Dedner, M. Hörl, and C. Rohde, “Dune-MMesh: The Dune Grid Module for Moving Interfaces,” J. Open Source Softw., vol. 7, no. 74, Art. no. 74, 2022, doi: 10.21105/joss.03959.
    3. J. Magiera and C. Rohde, “Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics,” in Droplet Dynamics under Extreme Ambient Conditions, K. Schulte, C. Tropea, and B. Weigand, Eds., in Droplet Dynamics under Extreme Ambient Conditions. Springer International Publishing, 2022. doi: 10.1007/978-3-031-09008-0_4.
    4. S. Burbulla and C. Rohde, “A finite-volume moving-mesh method for two-phase flow in fracturing porous media,” J. Comput. Phys., p. 111031, 2022, doi: https://doi.org/10.1016/j.jcp.2022.111031.
    5. F. Massa, L. Ostrowski, F. Bassi, and C. Rohde, “An artificial Equation of State based Riemann solver for a discontinuous Galerkin discretization of the incompressible Navier–Stokes equations,” J. Comput. Phys., p. 110705, 2022, doi: https://doi.org/10.1016/j.jcp.2021.110705.
    6. T. Mel’nyk and C. Rohde, “Asymptotic expansion for convection-dominated transport in a thin graph-like junction,” arXiv e-prints, 2022. doi: 10.48550/ARXIV.2208.05812.

  3. 2021

    1. C. Rohde and H. Tang, “On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena,” NoDEA Nonlinear Differential Equations Appl., vol. 28, no. 1, Art. no. 1, 2021, doi: 10.1007/s00030-020-00661-9.
    2. D. Alonso-Orán, C. Rohde, and H. Tang, “A local-in-time theory for singular SDEs with applications to fluid models with transport noise,” J. Nonlinear Sci., vol. 31, no. 6, Art. no. 6, 2021, doi: doi.org/10.1007/s00332-021-09755-9.
    3. C. Rohde and L. Von Wolff, “A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution,” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 01, Art. no. 01, 2021, doi: 10.1142/S0218202521500019.
    4. J. Dürrwächter, F. Meyer, T. Kuhn, A. Beck, C.-D. Munz, and C. Rohde, “A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations,” Computers & Fluids, vol. 228, pp. 1850044, 20, 2021, doi: 10.1016/j.compfluid.2021.105039.
    5. J. Giesselmann, F. Meyer, and C. Rohde, “Error control for statistical solutions of hyperbolic systems of conservation laws,” Calcolo, vol. 58, no. 2, Art. no. 2, 2021, doi: 10.1007/s10092-021-00417-6.
    6. M. Alkämper, J. Magiera, and C. Rohde, “An Interface Preserving Moving Mesh in Multiple SpaceDimensions,” Computing Research Repository, vol. abs/2112.11956, 2021, [Online]. Available: https://arxiv.org/abs/2112.11956
    7. L. von Wolff, F. Weinhardt, H. Class, J. Hommel, and C. Rohde, “Investigation of Crystal Growth in Enzymatically Induced Calcite Precipitation by Micro-Fluidic Experimental Methods and Comparison with Mathematical Modeling,” Transp. Porous Media, vol. 137, no. 2, Art. no. 2, 2021, doi: 10.1007/s11242-021-01560-y.
    8. A. Beck, J. Dürrwächter, T. Kuhn, F. Meyer, C.-D. Munz, and C. Rohde, “Uncertainty Quantification in High Performance Computational Fluid Dynamics,” in High Performance Computing in Science and Engineering ’19, W. E. Nagel, D. H. Kröner, and M. M. Resch, Eds., in High Performance Computing in Science and Engineering ’19. Cham: Springer International Publishing, 2021, pp. 355--371.
    9. C. Rohde and H. Tang, “On a stochastic Camassa-Holm type equation with higher order nonlinearities,” J. Dynam. Differential Equations, vol. 33, pp. 1823–1852, 2021, doi: https://doi.org/10.1007/s10884-020-09872-1.
    10. M. Gander, S. Lunowa, and C. Rohde, “Consistent and asymptotic-preserving finite-volume domain decomposition methods for singularly perturbed elliptic equations,” in Domain Decomposition Methods in Science and Engineering XXVI, in Domain Decomposition Methods in Science and Engineering XXVI. Lect. Notes Comput. Sci. Eng.,  Springer, Cham, 2021. [Online]. Available: http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf

  4. 2020

    1. A. Armiti-Juber and C. Rohde, “On the well-posedness of a nonlinear fourth-order extension of Richards’ equation,” J. Math. Anal. Appl., vol. 487, no. 2, Art. no. 2, 2020, doi: https://doi.org/10.1016/j.jmaa.2020.124005.
    2. S. Burbulla and C. Rohde, “A fully conforming finite volume approach to two-phase flow in fractured porous media,” in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F. A. Radu, and J. Fuhrmann, Eds., in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. Cham: Springer International Publishing, 2020, pp. 547–555. doi: https://doi.org/10.1007/978-3-030-43651-3_51.
    3. J. Giesselmann, F. Meyer, and C. Rohde, “An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws,” in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018, A. Bressan, M. Lewicka, D. Wang, and Y. Zheng, Eds., in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018, vol. 10. AIMS Series on Applied Mathematics, 2020, pp. 449–456. [Online]. Available: https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf
    4. J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws,” BIT Numer. Math., 2020, [Online]. Available: https://doi.org/10.1007/s10543-019-00794-z
    5. J. Magiera, D. Ray, J. S. Hesthaven, and C. Rohde, “Constraint-aware neural networks for Riemann problems,” J. Comput. Phys., vol. 409, no. 109345, Art. no. 109345, 2020, doi: https://doi.org/10.1016/j.jcp.2020.109345.
    6. 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,” SIAM J. Sci. Comput., vol. 42, no. 4, Art. no. 4, 2020, doi: https://doi.org/10.1137/18M1210575.
    7. T. Hitz, J. Keim, C.-D. Munz, and C. Rohde, “A parabolic relaxation model for the Navier-Stokes-Korteweg equations,” J. Comput. Phys., vol. 421, p. 109714, 2020, doi: https://doi.org/10.1016/j.jcp.2020.109714.
    8. C. Rohde and L. von Wolff, “Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media,” SIAM J. Math. Anal., vol. 52, no. 6, Art. no. 6, 2020, doi: 10.1137/19M1242434.
    9. 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., vol. 40, no. 2, Art. no. 2, 2020, doi: 10.1093/imanum/drz004.
    10. L. Ostrowski and C. Rohde, “Compressible multi-component flow in porous media with Maxwell-Stefan diffusion,” Math. Meth. Appl. Sci., pp. 1–22, 2020, [Online]. Available: https://doi.org/10.1002/mma.6185
    11. L. Ostrowski and C. Rohde, “Phase field modelling for compressible droplet impingement,” in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018, A. Bressan, M. Lewicka, D. Wang, and Y. Zheng, Eds., in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018, vol. 10. AIMS Series on Applied Mathematics, 2020, pp. 586–593. [Online]. Available: https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf
    12. L. Ostrowski, F. C. Massa, and C. Rohde, “A phase field approach to compressible droplet impingement,” in Droplet Interactions and Spray Processes, G. Lamanna, S. Tonini, G. E. Cossali, and B. Weigand, Eds., in Droplet Interactions and Spray Processes. Cham: Springer International Publishing, 2020, pp. 113–126. [Online]. Available: https://doi.org/10.1007/978-3-030-33338-6_9

  5. 2019

    1. D. Seus, F. A. Radu, and C. Rohde, “A linear domain decomposition method for two-phase flow in porous media,” Numerical Mathematics and Advanced Applications ENUMATH 2017, pp. 603–614, 2019, doi: https://doi.org/10.1007/978-3-319-96415-7_55.
    2. R. M. Colombo, P. G. LeFloch, C. Rohde, and K. Trivisa, “Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics,” Oberwohlfach Rep., no. 16, Art. no. 16, 2019, [Online]. Available: https://www.ems-ph.org/journals/show_issue.php?issn=1660-8933&vol=16&iss=2
    3. V. Sharanya, G. P. R. Sekhar, and C. Rohde, “Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow,” Physics of Fluids, vol. 31, no. 1, Art. no. 1, 2019, doi: 10.1063/1.5064694.
    4. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for  a carbon dioxide storage benchmark scenario,” Comput. Geosci., vol. 2, no. 23, Art. no. 23, 2019, doi: https://doi.org/10.1007/s10596-018-9785-x.
    5. T. Kuhn, J. Dürrwächter, F. Meyer, A. Beck, C. Rohde, and C.-D. Munz, “Uncertainty quantification for direct aeroacoustic simulations of cavity flows,” J. Theor. Comput. Acoust., vol. 27, no. 1, Art. no. 1, 2019, doi: https://doi.org/10.1142/S2591728518500445.
    6. A. Armiti-Juber and C. Rohde, “Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media,” J. Math. Anal. Appl., vol. 477, no. 1, Art. no. 1, 2019, doi: https://doi.org/10.1016/j.jmaa.2019.04.049.
    7. A. Armiti-Juber and C. Rohde, “On Darcy-and Brinkman-type models for two-phase flow in asymptotically flat domains,” Comput. Geosci., vol. 23, no. 2, Art. no. 2, 2019, doi: https://doi.org/10.1007/s10596-018-9756-2.

  6. 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, doi: http://dx.doi.org/10.1016/j.compfluid.2017.03.026.
    2. C. Rohde, “Fully resolved compressible two-phase flow : modelling, analytical and numerical issues,” in New trends and results in mathematical description of fluid flows, M. Bulicek, E. Feireisl, and M. Pokorný, Eds., in New trends and results in mathematical description of fluid flows. Basel: Birkhäuser, 2018, pp. 115–181. doi: 10.1007/978-3-319-94343-5.
    3. J. Magiera and C. Rohde, “A particle-based multiscale solver for compressible liquid-vapor flow,” Springer Proc. Math. Stat., pp. 291--304, 2018, doi: 10.1007/978-3-319-91548-7_23.
    4. V. Sharanya, G. P. R. Sekhar, and C. Rohde, “The low surface Péclet number regime for surfactant-laden viscous droplets: Influence of surfactant concentration, interfacial slip effects and cross migration,” Int. J. of Multiph. Flow, no. 107, Art. no. 107, Oct. 2018, doi: https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.008.
    5. C. Chalons, J. Magiera, C. Rohde, and M. Wiebe, “A finite-volume tracking scheme for two-phase compressible flow,” Springer Proc. Math. Stat., pp. 309--322, 2018, doi: https://doi.org/10.1007/978-3-319-91545-6_25.
    6. C. Rohde and C. Zeiler, “On Riemann solvers and kinetic relations for isothermal two-phase  flows with surface tension,” Z. Angew. Math. Phys., no. 3, Art. no. 3, 2018, doi: https://doi.org/10.1007/s00033-018-0958-1.
    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 Péclet number,” International Journal of Multiphase Flow, vol. 107, pp. 82–103, 2018, [Online]. Available: http://arxiv.org/abs/1609.03410
    8. D. Seus, I. S. Pop, C. Rohde, K. Mitra, and F. Radu, “A linear domain decompostition method for partially saturated flow in porous media,” Comput. Methods Appl. Mech. Eng., vol. 333, pp. 331–355, 2018, doi: https://doi.org/10.1016/j.cma.2018.01.029.
    9. D. Seus, K. Mitra, I. S. Pop, F. A. Radu, and C. Rohde, “A linear domain decomposition method for partially saturated flow  in porous media,” Comp. Methods Appl. Mech. Eng., vol. 333, pp. 331--355, 2018, doi: https://doi.org/10.1016/j.cma.2018.01.029.

  7. 2017

    1. S. Fechter, C.-D. Munz, C. Rohde, and C. Zeiler, “A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension,” J. Comput. Phys., vol. 336, pp. 347–374, May 2017, doi: 10.1016/j.jcp.2017.02.001.
    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, doi: 10.1007/s10596-017-9662-z.
    3. M. Kutter, C. Rohde, and A.-M. Sändig, “Well-posedness of a two scale model for liquid phase epitaxy with elasticity,” Contin. Mech. Thermodyn., vol. 29, no. 4, Art. no. 4, 2017, doi: 10.1007/s00161-015-0462-1.
    4. 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, Art. no. 5, Sep. 2017, doi: https://doi.org/10.1051/m2an/2017027.
    5. M. Köppel et al., “Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage.” Nov. 2017. doi: 10.5281/zenodo.933827.
    6. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” University of Stuttgart, 2017. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759

  8. 2016

    1. F. I. Dragomirescu, K. Eisenschmidt, C. Rohde, and B. Weigand, “Perturbation solutions for the finite radially symmetric Stefan problem,” INTERNATIONAL JOURNAL OF THERMAL SCIENCES, vol. 104, pp. 386–395, Jun. 2016, doi: 10.1016/j.ijthermalsci.2016.01.019.
    2. F. Betancourt and C. Rohde, “Finite-Volume Schemes for Friedrichs Systems with Involutions,” App. Math. Comput., vol. 272, Part 2, pp. 420–439, 2016, doi: 10.1016/j.amc.2015.03.050.
    3. 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, doi: https://doi.org/10.1093/imamat/hxw023.
    4. R. M. Colombo, P. G. LeFloch, and C. Rohde, “Hyperbolic techniques in Modelling, Analysis and Numerics,” Oberwolfach Reports, vol. 13, pp. 1683–1751, 2016, doi: 10.4171/OWR/2016/30.
    5. 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, no. 2, Art. no. 2, 2016, doi: 10.1016/j.amc.2015.09.080.
    6. J. Magiera, C. Rohde, and I. Rybak, “A hyperbolic-elliptic model problem for coupled surface-subsurface  flow,” Transp. Porous Media, vol. 114, pp. 425–455, 2016, doi: 10.1007/S11242-015-0548-Z.
    7. 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, doi: https://doi.org/10.1016/j.ijthermalsci.2016.01.019.
    8. M. Dumbser, G. Gassner, C. Rohde, and S. Roller, “Preface to the special issue ``Recent Advances in Numerical Methods for    Hyperbolic Partial Differential Equations’’,” APPLIED MATHEMATICS AND COMPUTATION, vol. 272, no. 2, Art. no. 2, Jan. 2016, doi: 10.1016/j.amc.2015.11.023.
    9. A. Barth, R. Bürger, I. Kröker, and C. Rohde, “Computational uncertainty quantification for a clarifier-thickener  model with several random perturbations: A hybrid stochastic Galerkin  approach,” Computers & Chemical Engineering, vol. 89, pp. 11-- 26, 2016, doi: http://dx.doi.org/10.1016/j.compchemeng.2016.02.016.
    10. V. Sharanya, G. P. R. Sekhar, and C. Rohde, “Bed of polydisperse viscous spherical drops under thermocapillary    effects,” ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, vol. 67, no. 4, Art. no. 4, Aug. 2016, doi: 10.1007/s00033-016-0699-y.
    11. B. Kabil and C. Rohde, “Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension,” Math. Meth. Appl. Sci., vol. 39, no. 18, Art. no. 18, 2016, doi: 10.1002/mma.3926.
    12. M. Köppel and C. Rohde, “Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous  Media,” PAMM Proc. Appl. Math. Mech., vol. 16, no. 1, Art. no. 1, 2016, doi: 10.1002/pamm.201610363.
    13. 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, no. 2, Art. no. 2, 2016, doi: 10.1016/j.amc.2015.09.080.

  9. 2015

    1. 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, doi: 10.1002/fld.4065.
    2. 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, Apr. 2015, doi: 10.1007/s10596-015-9469-8.
    3. C. Rohde and C. Zeiler, “A relaxation Riemann solver for compressible two-phase flow with phase    transition and surface tension,” APPLIED NUMERICAL MATHEMATICS, vol. 95, no. SI, Art. no. SI, Sep. 2015, doi: 10.1016/j.apnum.2014.05.001.
    4. 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, Art. no. 12, Dec. 2015, doi: 10.1002/fld.4065.
    5. 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, Art. no. 2, 2015, doi: 10.1007/s10596-014-9464-5.
    6. F. Kissling and C. Rohde, “THE COMPUTATION OF NONCLASSICAL SHOCK WAVES IN POROUS MEDIA WITH A    HETEROGENEOUS MULTISCALE METHOD: THE MULTIDIMENSIONAL CASE,” MULTISCALE MODELING & SIMULATION, vol. 13, no. 4, Art. no. 4, 2015, doi: 10.1137/120899236.
    7. I. Kroeker, W. Nowak, and C. Rohde, “A stochastically and spatially adaptive parallel scheme for uncertain    and nonlinear two-phase flow problems,” COMPUTATIONAL GEOSCIENCES, vol. 19, no. 2, Art. no. 2, Apr. 2015, doi: 10.1007/s10596-014-9464-5.

  10. 2014

    1. W. Ehlers, R. Helmig, and C. Rohde, “Editorial: Deformation and transport phenomena in porous media,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 94, no. 7–8, Art. no. 7–8, 2014, doi: 10.1002/zamm.201400559.
    2. 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, Art. no. 10, 2014, doi: 10.1002/zamm.201200174.
    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, Art. no. 1, 2014, [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=732
    4. M. Köppel, I. Kröker, and C. Rohde, “Stochastic Modeling for Heterogeneous Two-Phase Flow,” in Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects, J. Fuhrmann, M. Ohlberger, and C. Rohde, Eds., in Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects, vol. 77. Springer International Publishing, 2014, pp. 353–361. doi: 10.1007/978-3-319-05684-5_34.
    5. B. Kabil and C. Rohde, “The influence of surface tension and configurational forces on the  stability of liquid-vapor interfaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 107, no. 0, Art. no. 0, 2014, [Online]. Available: http://dx.doi.org/10.1016/j.na.2014.04.003
    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, J. Fuhrmann, M. Ohlberger, and C. Rohde, Eds., in Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, vol. 78. Springer International Publishing, 2014, pp. 873–881. doi: 10.1007/978-3-319-05591-6_88.
    7. P. Engel, A. Viorel, and C. Rohde, “A Low-Order Approximation for Viscous-Capillary Phase Transition  Dynamics,” Port. Math., vol. 70, no. 4, Art. no. 4, 2014, [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=723
    8. 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, in ILASS Europe, 26th European Conference on Liquid Atomization and Spray Systems. 2014.
    9. A. Corli, C. Rohde, and V. Schleper, “Parabolic approximations of diffusive-dispersive equations.,” J. Math. Anal. Appl., vol. 414, pp. 773–798, 2014, [Online]. Available: http://dx.doi.org/10.1016/j.jmaa.2014.01.049

  11. 2013

    1. Ch. Eck, M. Kutter, A.-M. Sändig, and Ch. Rohde, “A two scale model for liquid phase epitaxy with elasticity: An iterative  procedure,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift  für Angewandte Mathematik und Mechanik, vol. 93, no. 10–11, Art. no. 10–11, 2013, doi: 10.1002/zamm.201200238.
    2. 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, Art. no. 5, 2013, doi: 10.3934/cpaa.2013.12.2145.
    3. 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, Art. no. 03, 2013, doi: 10.1142/S0218202512500522.
    4. 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, in ILASS�Europe, 25th European Conference on Liquid Atomization and  Spray Systems. 2013.

  12. 2012

    1. P. Engel and C. Rohde, “On the Space-Time Expansion Discontinuous Galerkin Method,” in Hyperbolic Problems: Theory, Numerics and Applications, T. Li and S. Jiang, Eds., in Hyperbolic Problems: Theory, Numerics and Applications. 2012, pp. 406--414.
    2. 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, Art. no. 3, 2012, doi: 10.1137/110848815.
    3. 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, doi: 10.1051/proc/201238022.
    4. 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, Art. no. 3, 2012, doi: 10.2136/vzj2011.0193.
    5. I. Kröker and C. Rohde, “Finite volume schemes for hyperbolic balance laws with multiplicative  noise,” Appl. Numer. Math., vol. 62, no. 4, Art. no. 4, 2012, doi: 10.1016/j.apnum.2011.01.011.
    6. T. Richter et al., “ViPLab: a virtual programming laboratory for mathematics and engineering,” Interactive Technology and Smart Education, vol. 9, pp. 246–262, 2012, doi: 10.1108/17415651211284039.
    7. A. Corli and C. Rohde, “Singular limits for a parabolic-elliptic regularization of scalar conservation laws,” J. Differential Equations, vol. 253, no. 5, Art. no. 5, 2012, doi: 10.1016/j.jde.2012.05.006.
    8. W. Dreyer, J. Giesselmann, C. Kraus, and C. Rohde, “Asymptotic Analysis for Korteweg Models,” Interfaces Free Bound., vol. 14, pp. 105–143, 2012, [Online]. Available: http://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=14&iss=1&rank=4
    9. 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, T. Li and S. Jiang, Eds., in Hyperbolic Problems: Theory, Numerics and Applications. 2012, pp. 469--478.
    10. 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, Art. no. 5, 2012, doi: 10.1002/mma.1593.

  13. 2011

    1. Th. Richter et al., “ViPLab - A Virtual Programming Laboratory for Mathematics and Engineering,” in Proceedings of the 2011 IEEE International Symposium on Multimedia, in Proceedings of the 2011 IEEE International Symposium on Multimedia. Washington, DC, USA: IEEE Computer Society, 2011, pp. 537--542. doi: 10.1109/ISM.2011.95.
    2. 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, in Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2, vol. 4. Springer, 2011, pp. 195--203. doi: 10.1007/978-3-642-20671-9_21.

  14. 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, Art. no. 3, 2010, doi: 10.3934/nhm.2010.5.661.
    2. C. Rohde, “A local and low-order Navier-Stokes-Korteweg system,” in Nonlinear partial differential equations and hyperbolic wave phenomena, in Nonlinear partial differential equations and hyperbolic wave phenomena, vol. 526. Providence, RI: Amer. Math. Soc., 2010, pp. 315--337. doi: 10.1090/conm/526/10387.

  15. 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, Art. no. 12, 2009, doi: 10.1016/j.jde.2009.05.006.

  16. 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, in Hyperbolic problems: theory, numerics, applications. Berlin: Springer, 2008, pp. 891--899. doi: 10.1007/978-3-540-75712-2_93.
    2. 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, Art. no. 2, 2008, doi: 10.1512/iumj.2008.57.3271.
    3. A. Dressel and C. Rohde, “A finite-volume approach to liquid-vapour fluids with phase transition,” in Finite volumes for complex applications V, in Finite volumes for complex applications V. ISTE, London, 2008, pp. 53--68.
    4. 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, Art. no. 12, 2008, doi: 10.1142/S0218202508003327.
    5. 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, [Online]. Available: https://www.researchgate.net/profile/Christian_Rohde2/publication/228406932_Local_discontinuous-Galerkin_schemes_for_model_problems_in_phase_transition_theory/links/00b4952cb030e0da90000000.pdf

  17. 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, Art. no. 1, 2007, doi: 10.1016/j.jde.2006.11.010.
    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, Art. no. 6, 2007, doi: 10.1051/m2an:2007048.

  18. 2006

    1. J. Haink and C. Rohde, “Phase transition in compressible media and nonlocal capillarity terms,” in Hyperbolic problems: theory, numerics and applications. I, in Hyperbolic problems: theory, numerics and applications. I. Yokohama Publ., Yokohama, 2006, pp. 147--154.
    2. 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, Art. no. 6, 2006, doi: 10.1137/S0036142903438136.
    3. D. Diehl and C. Rohde, “On the structure of MHD shock waves in diffusive-dispersive media,” J. Math. Fluid Mech., vol. 8, no. 1, Art. no. 1, 2006, doi: 10.1007/s00021-004-0149-z.
    4. C. Merkle and C. Rohde, “Computation of dynamical phase transitions in solids,” Appl. Numer. Math., vol. 56, no. 10–11, Art. no. 10–11, 2006, doi: 10.1016/j.apnum.2006.03.025.

  19. 2005

    1. 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, in Numerical methods for hyperbolic and kinetic problems, vol. 7. Eur. Math. Soc., Zürich, 2005, pp. 239--270. doi: 10.4171/012-1/11.
    2. M. J. Gander and C. Rohde, “Nonlinear advection problems and overlapping Schwarz waveform relaxation,” in Domain decomposition methods in science and engineering, in Domain decomposition methods in science and engineering, vol. 40. Berlin: Springer, 2005, pp. 251--258. doi: 10.1007/3-540-26825-1_23.
    3. C. Rohde, “Scalar conservation laws with mixed local and nonlocal diffusion-dispersion  terms,” SIAM J. Math. Anal., vol. 37, no. 1, Art. no. 1, 2005, doi: 10.1137/S0036141004443300.
    4. C. Rohde, “Phase transitions and sharp-interface limits for the 1d-elasticity  system with non-local energy,” Interfaces Free Bound., vol. 7, no. 1, Art. no. 1, 2005, doi: 10.4171/IFB/116.
    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, Art. no. 12, 2005, doi: 10.1002/zamm.200410211.
    6. 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, in Analysis and numerics for conservation laws. Berlin: Springer, 2005, pp. 163--202. doi: 10.1007/3-540-27907-5_8.
    7. M. J. Gander and C. Rohde, “Overlapping Schwarz waveform relaxation for convection-dominated  nonlinear conservation laws,” SIAM J. Sci. Comput., vol. 27, no. 2, Art. no. 2, 2005, doi: 10.1137/030601090.
    8. 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, Art. no. 1, 2005, doi: 10.1002/num.20026.

  20. 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, Art. no. 2, 2004, doi: 10.1007/s00791-004-0140-5.
    2. A. Dedner and C. Rohde, “Numerical approximation of entropy solutions for hyperbolic integro-differential  equations,” Numer. Math., vol. 97, no. 3, Art. no. 3, 2004, doi: 10.1007/s00211-003-0502-9.
    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, Art. no. 4, 2004, doi: 10.1142/S0219891604000329.

  21. 2003

    1. A. Dedner, C. Rohde, and M. Wesenberg, “Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics,” in Hyperbolic problems: theory, numerics, applications, in Hyperbolic problems: theory, numerics, applications. Berlin: Springer, 2003, pp. 499--508.
    2. A. Dedner, C. Rohde, and M. Wesenberg, “A new approach to divergence cleaning in magnetohydrodynamic simulations,” in Hyperbolic problems: theory, numerics, applications, in Hyperbolic problems: theory, numerics, applications. Berlin: Springer, 2003, pp. 509--518.
    3. 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, in Trends in nonlinear analysis. Berlin: Springer, 2003, pp. 289--306.
    4. 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, in Geometric analysis and nonlinear partial differential equations. Berlin: Springer, 2003, pp. 573--589.
    5. 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, Art. no. 4, 2003, doi: 10.1023/A:1026010631074.
    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, Art. no. 2, 2003, doi: 10.1016/S0167-2789(03)00206-9.

  22. 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), in Finite volumes for complex applications, III (Porquerolles, 2002). Hermes Sci. Publ., Paris, 2002, pp. 165--172.
    2. M. Ohlberger and C. Rohde, “Adaptive finite volume approximations for weakly coupled convection  dominated parabolic systems,” IMA J. Numer. Anal., vol. 22, no. 2, Art. no. 2, 2002, doi: 10.1093/imanum/22.2.253.
    3. 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, Art. no. 5, 2002, doi: 10.1137/S003614290240069X.
    4. H. Freistühler and C. Rohde, “Numerical computation of viscous profiles for hyperbolic conservation  laws,” Math. Comp., vol. 71, no. 239, Art. no. 239, 2002, doi: 10.1090/S0025-5718-01-01340-0.

  23. 2001

    1. 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, in Ergodic theory, analysis, and efficient simulation of dynamical systems. Berlin: Springer, 2001, pp. 287--309, 814.
    2. 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, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.
    3. 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, Art. no. 1, 2001, doi: 10.1006/jmaa.2001.7447.
    4. 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, Art. no. 4, 2001, doi: 10.1512/iumj.2001.50.2057.
    5. A. Dedner, D. Kröner, C. Rohde, and M. Wesenberg, “Godunov-type schemes for the MHD equations,” in Godunov methods (Oxford, 1999), in Godunov methods (Oxford, 1999). Kluwer/Plenum, New York, 2001, pp. 209--216.
    6. 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), in Hyperbolic problems: theory, numerics, applications, Vol. I,  II (Magdeburg, 2000), vol. 141. Basel: Birkhäuser, 2001, pp. 399--408.
    7. 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), in Hyperbolic problems: theory, numerics, applications, Vol. I,  II (Magdeburg, 2000), vol. 141. Basel: Birkhäuser, 2001, pp. 277--286.
    8. 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, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.

  24. 2000

    1. P. G. Lefloch and C. Rohde, “High-order schemes, entropy inequalities, and nonclassical shocks,” SIAM J. Numer. Anal., vol. 37, no. 6, Art. no. 6, 2000, doi: 10.1137/S0036142998345256.

  25. 1999

    1. 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), in Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich,  1998), vol. 129. Basel: Birkhäuser, 1999, pp. 333--342.
    2. A. Dedner, C. Rohde, and M. Wesenberg, “A MHD-simulation in solar physics,” in Finite volumes for complex applications II, in Finite volumes for complex applications II. Hermes Sci. Publ., Paris, 1999, pp. 491--498.

  26. 1998

    1. C. Rohde, “Entropy solutions for weakly coupled hyperbolic systems in several  space dimensions,” Z. Angew. Math. Phys., vol. 49, no. 3, Art. no. 3, 1998, doi: 10.1007/s000000050102.
    2. C. Rohde, “Upwind finite volume schemes for weakly coupled hyperbolic systems  of conservation laws in 2D,” Numer. Math., vol. 81, no. 1, Art. no. 1, 1998, doi: 10.1007/s002110050385.
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