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
+49 711 685 65599

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.131

Office Hours

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

  1. 2024

    1. Alkämper, M., Magiera, J., Rohde, C.: An Interface-Preserving Moving Mesh in Multiple Space  Dimensions. ACM Trans. Math. Softw. 50, (2024). https://doi.org/10.1145/3630000.
    2. Hörl, M., Rohde, C.: Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture. Netw. Heterog. Media. 19, 114–156 (2024). https://doi.org/10.3934/nhm.2024006.
    3. Magiera, J., Rohde, C.: A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate. Communications on Applied Mathematics and Computation. (2024). https://doi.org/10.1007/s42967-023-00349-8.
    4. Mel’nyk, T., Rohde, C.: Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains, https://arxiv.org/html/2404.07538v1, (2024).
    5. Mel’nyk, T., Rohde, C.: Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks. J. Math. Anal. Appl. 529, Paper No. 127587, 35 (2024). https://doi.org/10.1016/j.jmaa.2023.127587.
    6. Mel’nyk, T., Rohde, C.: Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: strong boundary interactions. Asymptotic Analysis. 137, 27–52 (2024). https://doi.org/10.3233/ASY-231876.
    7. Mel’nyk, T., Rohde, C.: Asymptotic expansion for convection-dominated transport in a thin graph-like junction. Analysis and Applications. 22, 833–879 (2024). https://doi.org/10.1142/S0219530524500040.
    8. Miao, Y., Rohde, C., Tang, H.: Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities. Stoch. Partial Differ. Equ. Anal. Comput. 12, 614–674 (2024). https://doi.org/10.1007/s40072-023-00291-z.
  2. 2023

    1. Burbulla, S., Formaggia, L., Rohde, C., Scotti, A.: Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models. Comput. Methods Appl. Mech. Engrg. 403, (2023). https://doi.org/10.1016/j.cma.2022.115699.
    2. Burbulla, S., Hörl, M., Rohde, C.: Flow in Porous Media with Fractures of Varying Aperture. SIAM J. Sci. Comput. 45, A1519–A1544 (2023). https://doi.org/10.1137/22M1510406.
    3. Gander, M.J., Lunowa, S.B., Rohde, C.: Consistent and Asymptotic-Preserving Finite-Volume Robin Transmission Conditions for Singularly Perturbed Elliptic Equations. In: Brenner, S.C., Chung, E., Klawonn, A., Kwok, F., Xu, J., and Zou, J. (eds.) Domain Decomposition Methods in Science and Engineering XXVI. pp. 443--450. Springer International Publishing, Cham (2023).
    4. Gander, M.J., Lunowa, S.B., Rohde, C.: Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations. SIAM J. Sci. Comput. 45, A49–A73 (2023). https://doi.org/10.1137/21M1415005.
    5. Keim, J., Schwarz, A., Chiocchetti, S., Rohde, C., Beck, A.: A Reinforcement Learning Based Slope Limiter for Two-Dimensional Finite Volume Schemes. (2023). https://doi.org/10.13140/RG.2.2.18046.87363.
    6. Keim, J., Munz, C.-D., Rohde, C.: A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in Confined Domains. J. Comput. Phys. 474, 111830 (2023). https://doi.org/10.1016/j.jcp.2022.111830.
    7. Seus, D., Radu, F.A., Rohde, C.: Towards hybrid two-phase modelling using linear domain decomposition. Numer. Methods Partial Differential Equations. 39, 622–656 (2023). https://doi.org/10.1002/num.22906.
  3. 2022

    1. Burbulla, S., Dedner, A., Hörl, M., Rohde, C.: Dune-MMesh: The Dune Grid Module for Moving Interfaces. J. Open Source Softw. 7, 3959 (2022). https://doi.org/10.21105/joss.03959.
    2. Burbulla, S., Rohde, C.: A finite-volume moving-mesh method for two-phase flow in fracturing porous media. J. Comput. Phys. 111031 (2022). https://doi.org/10.1016/j.jcp.2022.111031.
    3. Magiera, J., Rohde, C.: A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces. J. Comput. Phys. 111551 (2022). https://doi.org/10.1016/j.jcp.2022.111551.
    4. Magiera, J., Rohde, C.: Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics. In: Schulte, K., Tropea, C., and Weigand, B. (eds.) Droplet Dynamics under Extreme Ambient Conditions. Springer International Publishing (2022). https://doi.org/10.1007/978-3-031-09008-0_4.
    5. Massa, F., Ostrowski, L., Bassi, F., Rohde, C.: An artificial Equation of State based Riemann solver for a discontinuous Galerkin discretization of the incompressible Navier–Stokes equations. J. Comput. Phys. 110705 (2022). https://doi.org/10.1016/j.jcp.2021.110705.
  4. 2021

    1. Alonso-Orán, D., Rohde, C., Tang, H.: A local-in-time theory for singular SDEs with applications to fluid models with transport noise. J. Nonlinear Sci. 31, Paper No. 98, 55 (2021). https://doi.org/doi.org/10.1007/s00332-021-09755-9.
    2. Beck, A., Dürrwächter, J., Kuhn, T., Meyer, F., Munz, C.-D., Rohde, C.: Uncertainty Quantification in High Performance Computational Fluid Dynamics. In: Nagel, W.E., Kröner, D.H., and Resch, M.M. (eds.) High Performance Computing in Science and Engineering ’19. pp. 355--371. Springer International Publishing, Cham (2021).
    3. Dürrwächter, J., Meyer, F., Kuhn, T., Beck, A., Munz, C.-D., Rohde, C.: A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations. Computers & Fluids. 228, 1850044, 20 (2021). https://doi.org/10.1016/j.compfluid.2021.105039.
    4. Gander, M., Lunowa, S., Rohde, C.: Consistent and asymptotic-preserving finite-volume domain decomposition methods for singularly perturbed elliptic equations. In: Domain Decomposition Methods in Science and Engineering XXVI. Lect. Notes Comput. Sci. Eng.,  Springer, Cham (2021).
    5. Giesselmann, J., Meyer, F., Rohde, C.: Error control for statistical solutions of hyperbolic systems of conservation laws. Calcolo. 58, Paper No. 23, 29 (2021). https://doi.org/10.1007/s10092-021-00417-6.
    6. Rohde, C., Tang, H.: On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena. NoDEA Nonlinear Differential Equations Appl. 28, Paper No. 5, 34 (2021). https://doi.org/10.1007/s00030-020-00661-9.
    7. Rohde, C., Tang, H.: On a stochastic Camassa-Holm type equation with higher order nonlinearities. J. Dynam. Differential Equations. 33, 1823–1852 (2021). https://doi.org/10.1007/s10884-020-09872-1.
    8. Rohde, C., Von Wolff, L.: A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution. Mathematical Models and Methods in Applied Sciences. 31, 1–35 (2021). https://doi.org/10.1142/S0218202521500019.
    9. von Wolff, L., Weinhardt, F., Class, H., Hommel, J., Rohde, C.: Investigation of Crystal Growth in Enzymatically Induced Calcite Precipitation by Micro-Fluidic Experimental Methods and Comparison with Mathematical Modeling. Transp. Porous Media. 137, 327--343 (2021). https://doi.org/10.1007/s11242-021-01560-y.
  5. 2020

    1. Armiti-Juber, A., Rohde, C.: On the well-posedness of a nonlinear fourth-order extension of Richards’ equation. J. Math. Anal. Appl. 487, 124005 (2020). https://doi.org/10.1016/j.jmaa.2020.124005.
    2. Beck, A., Dürrwächter, J., Kuhn, T., Meyer, F., Munz, C.-D., Rohde, C.: $hp$-Multilevel Monte Carlo methods for uncertainty quantification of compressible flows. SIAM J. Sci. Comput. 42, B1067–B1091 (2020). https://doi.org/10.1137/18M1210575.
    3. Burbulla, S., Rohde, C.: A fully conforming finite volume approach to two-phase flow in fractured porous media. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., and Fuhrmann, J. (eds.) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. pp. 547–555. Springer International Publishing, Cham (2020). https://doi.org/10.1007/978-3-030-43651-3_51.
    4. Giesselmann, J., Meyer, F., Rohde, C.: An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws. In: Bressan, A., Lewicka, M., Wang, D., and Zheng, Y. (eds.) Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018. pp. 449–456. AIMS Series on Applied Mathematics (2020).
    5. Giesselmann, J., Meyer, F., Rohde, C.: A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws. BIT Numer. Math. (2020).
    6. Giesselmann, J., Meyer, F., Rohde, C.: A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method. IMA J. Numer. Anal. 40, 1094–1121 (2020). https://doi.org/10.1093/imanum/drz004.
    7. Hitz, T., Keim, J., Munz, C.-D., Rohde, C.: A parabolic relaxation model for the Navier-Stokes-Korteweg equations. J. Comput. Phys. 421, 109714 (2020). https://doi.org/10.1016/j.jcp.2020.109714.
    8. Magiera, J., Ray, D., Hesthaven, J.S., Rohde, C.: Constraint-aware neural networks for Riemann problems. J. Comput. Phys. 409, (2020). https://doi.org/10.1016/j.jcp.2020.109345.
    9. Ostrowski, L., Massa, F.C., Rohde, C.: A phase field approach to compressible droplet impingement. In: Lamanna, G., Tonini, S., Cossali, G.E., and Weigand, B. (eds.) Droplet Interactions and Spray Processes. pp. 113–126. Springer International Publishing, Cham (2020).
    10. Ostrowski, L., Rohde, C.: Compressible multicomponent flow in porous media with Maxwell-Stefan diffusion. Math. Meth. Appl. Sci. 43, 4200–4221 (2020). https://doi.org/10.1002/mma.6185.
    11. Ostrowski, L., Rohde, C.: Phase field modelling for compressible droplet impingement. In: Bressan, A., Lewicka, M., Wang, D., and Zheng, Y. (eds.) Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018. pp. 586–593. AIMS Series on Applied Mathematics (2020).
    12. Rohde, C., von Wolff, L.: Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media. SIAM J. Math. Anal. 52, 6155–6179 (2020). https://doi.org/10.1137/19M1242434.
  6. 2019

    1. Armiti-Juber, A., Rohde, C.: On Darcy-and Brinkman-type models for two-phase flow in asymptotically flat domains. Comput. Geosci. 23, 285–303 (2019). https://doi.org/10.1007/s10596-018-9756-2.
    2. Armiti-Juber, A., Rohde, C.: Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media. J. Math. Anal. Appl. 477, 592–612 (2019). https://doi.org/10.1016/j.jmaa.2019.04.049.
    3. Colombo, R.M., LeFloch, P.G., Rohde, C., Trivisa, K.: Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics. Oberwohlfach Rep. 1419–1497 (2019).
    4. Kuhn, T., Dürrwächter, J., Meyer, F., Beck, A., Rohde, C., Munz, C.-D.: Uncertainty quantification for direct aeroacoustic simulations of cavity flows. J. Theor. Comput. Acoust. 27, 1850044, 20 (2019). https://doi.org/10.1142/S2591728518500445.
    5. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Santin, G., Wittwar, D., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., Rohde, C.: Comparison of data-driven uncertainty quantification methods for  a carbon dioxide storage benchmark scenario. Comput. Geosci. 2, 339–354 (2019). https://doi.org/10.1007/s10596-018-9785-x.
    6. Seus, D., Radu, F.A., Rohde, C.: A linear domain decomposition method for two-phase flow in porous media. Numerical Mathematics and Advanced Applications ENUMATH 2017. 603–614 (2019). https://doi.org/10.1007/978-3-319-96415-7_55.
    7. Sharanya, V., Sekhar, G.P.R., Rohde, C.: Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow. Physics of Fluids. 31, 012110 (2019). https://doi.org/10.1063/1.5064694.
  7. 2018

    1. Chalons, C., Magiera, J., Rohde, C., Wiebe, M.: A finite-volume tracking scheme for two-phase compressible flow. Springer Proc. Math. Stat. 309--322 (2018). https://doi.org/10.1007/978-3-319-91545-6_25.
    2. Fechter, S., Munz, C.-D., Rohde, C., Zeiler, C.: Approximate Riemann solver for compressible liquid vapor flow with  phase transition and surface tension. Comput. & Fluids. 169, 169–185 (2018). http://dx.doi.org/10.1016/j.compfluid.2017.03.026.
    3. Magiera, J., Rohde, C.: A particle-based multiscale solver for compressible liquid-vapor flow. Springer Proc. Math. Stat. 291--304 (2018). https://doi.org/10.1007/978-3-319-91548-7_23.
    4. Raja Sekhar, G.P., Sharanya, V., Rohde, C.: Effect of surfactant concentration and interfacial slip on the flow  past a viscous drop at low surface Péclet number. International Journal of Multiphase Flow. 107, 82–103 (2018).
    5. Rohde, C., Zeiler, C.: On Riemann solvers and kinetic relations for isothermal two-phase  flows with surface tension. Z. Angew. Math. Phys. 69, Art. 76 (2018). https://doi.org/10.1007/s00033-018-0958-1.
    6. Rohde, C.: Fully resolved compressible two-phase flow : modelling, analytical and numerical issues. In: Bulicek, M., Feireisl, E., and Pokorný, M. (eds.) New trends and results in mathematical description of fluid flows. pp. 115–181. Birkhäuser, Basel (2018). https://doi.org/10.1007/978-3-319-94343-5.
    7. Seus, D., Mitra, K., Pop, I.S., Radu, F.A., Rohde, C.: A linear domain decomposition method for partially saturated flow  in porous media. Comp. Methods Appl. Mech. Eng. 333, 331--355 (2018). https://doi.org/10.1016/j.cma.2018.01.029.
    8. Seus, D., Pop, I.S., Rohde, C., Mitra, K., Radu, F.: A linear domain decompostition method for partially saturated flow in porous media. Comput. Methods Appl. Mech. Eng. 333, 331–355 (2018). https://doi.org/10.1016/j.cma.2018.01.029.
    9. Sharanya, V., Sekhar, G.P.R., Rohde, C.: 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. 82–103 (2018). https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.008.
  8. 2017

    1. Chalons, C., Rohde, C., Wiebe, M.: A finite volume method for undercompressive shock waves in two space dimensions. ESAIM Math. Model. Numer. Anal. 51, 1987–2015 (2017). https://doi.org/10.1051/m2an/2017027.
    2. Fechter, S., Munz, C.-D., Rohde, C., Zeiler, C.: A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension. J. Comput. Phys. 336, 347–374 (2017). https://doi.org/10.1016/j.jcp.2017.02.001.
    3. Kutter, M., Rohde, C., Sändig, A.-M.: Well-posedness of a two scale model for liquid phase epitaxy with elasticity. Contin. Mech. Thermodyn. 29, 989–1016 (2017). https://doi.org/10.1007/s00161-015-0462-1.
    4. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Santin, G., Wittwar, D., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., Rohde, C.: Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario. University of Stuttgart (2017).
    5. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Wittwar, D., Santin, G., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., Rohde, C.: Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage, https://doi.org/10.5281/zenodo.933827, (2017). https://doi.org/10.5281/zenodo.933827.
    6. Köppel, M., Kröker, I., Rohde, C.: Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems  Governing Two-Phase Flow in Heterogeneous Porous Media. Comput. Geosci. 21, 807–832 (2017). https://doi.org/10.1007/s10596-017-9662-z.
  9. 2016

    1. Barth, A., Bürger, R., Kröker, I., Rohde, C.: Computational uncertainty quantification for a clarifier-thickener  model with several random perturbations: A hybrid stochastic Galerkin  approach. Computers & Chemical Engineering. 89, 11-- 26 (2016). http://dx.doi.org/10.1016/j.compchemeng.2016.02.016.
    2. Betancourt, F., Rohde, C.: Finite-Volume Schemes for Friedrichs Systems with Involutions. App. Math. Comput. 272, Part 2, 420–439 (2016). https://doi.org/10.1016/j.amc.2015.03.050.
    3. Colombo, R.M., LeFloch, P.G., Rohde, C.: Hyperbolic techniques in Modelling, Analysis and Numerics. Oberwolfach Reports. 13, 1683–1751 (2016). https://doi.org/10.4171/OWR/2016/30.
    4. Diehl, D., Kremser, J., Kröner, D., Rohde, C.: Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions. Appl. Math. Comput. 272, 309–335 (2016). https://doi.org/10.1016/j.amc.2015.09.080.
    5. Diehl, D., Kremser, J., Kröner, D., Rohde, C.: Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions. Appl. Math. Comput. 272, 309–335 (2016). https://doi.org/10.1016/j.amc.2015.09.080.
    6. Dragomirescu, F.I., Eisenschmidt, K., Rohde, C., Weigand, B.: Perturbation solutions for the finite radially symmetric Stefan problem. INTERNATIONAL JOURNAL OF THERMAL SCIENCES. 104, 386–395 (2016). https://doi.org/10.1016/j.ijthermalsci.2016.01.019.
    7. Dragomirescu, I., Eisenschmidt, K., Rohde, C., Weigand, B.: Perturbation solutions for the finite radially symmetric Stefan problem. Inter. J. Thermal Sci. 104, 386–395 (2016). https://doi.org/10.1016/j.ijthermalsci.2016.01.019.
    8. Dumbser, M., Gassner, G., Rohde, C., Roller, S.: Preface to the special issue ``Recent Advances in Numerical Methods for    Hyperbolic Partial Differential Equations’’. APPLIED MATHEMATICS AND COMPUTATION. 272, 235–236 (2016). https://doi.org/10.1016/j.amc.2015.11.023.
    9. Kabil, B., Rohde, C.: Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension. Math. Meth. Appl. Sci. 39, 5409--5426 (2016). https://doi.org/10.1002/mma.3926.
    10. Köppel, M., Rohde, C.: Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous  Media. PAMM Proc. Appl. Math. Mech. 16, 749–750 (2016). https://doi.org/10.1002/pamm.201610363.
    11. Magiera, J., Rohde, C., Rybak, I.: A hyperbolic-elliptic model problem for coupled surface-subsurface  flow. Transp. Porous Media. 114, 425–455 (2016). https://doi.org/10.1007/S11242-015-0548-Z.
    12. Redeker, M., Pop, I.S., Rohde, C.: Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous  Media. IMA J. Appl. Math. 81(5), 898–939 (2016). https://doi.org/10.1093/imamat/hxw023.
    13. Sharanya, V., Raja Sekhar, G.P., Rohde, C.: Bed of polydisperse viscous spherical drops under thermocapillary  effects. Z. Angew. Math. Phys. 67, 101 (2016). https://doi.org/10.1007/s00033-016-0699-y.
  10. 2015

    1. Kissling, F., Rohde, C.: The Computation of Nonclassical Shock Waves in Porous Media with  a Heterogeneous Multiscale Method: The Multidimensional Case. Multiscale Model. Simul. 13 no. 4, 1507–1541 (2015). https://doi.org/10.1137/120899236.
    2. Kroeker, I., Nowak, W., Rohde, C.: A stochastically and spatially adaptive parallel scheme for uncertain    and nonlinear two-phase flow problems. COMPUTATIONAL GEOSCIENCES. 19, 269–284 (2015). https://doi.org/10.1007/s10596-014-9464-5.
    3. Kröker, I., Nowak, W., Rohde, C.: A stochastically and spatially adaptive parallel scheme for uncertain  and nonlinear two-phase flow problems. Comput. Geosci. 19, 269--284 (2015). https://doi.org/10.1007/s10596-014-9464-5.
    4. Neusser, J., Rohde, C., Schleper, V.: Relaxation of the Navier-Stokes-Korteweg Equations for Compressible  Two-Phase Flow with Phase Transition. J. Numer. Methods Fluids. 79, 615–639 (2015). https://doi.org/10.1002/fld.4065.
    5. Neusser, J., Rohde, C., Schleper, V.: Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase  flow with phase transition. J. Numer. Meth. Fluids. 79, 615–639 (2015). https://doi.org/10.1002/fld.4065.
    6. Rohde, C., Zeiler, C.: A relaxation Riemann solver for compressible two-phase flow with  phase transition and surface tension. Appl. Numer. Math. 95, 267--279 (2015). https://doi.org/10.1016/j.apnum.2014.05.001.
    7. Rybak, I., Magiera, J., Helmig, R., Rohde, C.: Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems. Comput. Geosci. 19, 299–309 (2015). https://doi.org/10.1007/s10596-015-9469-8.
  11. 2014

    1. Armiti-Juber, A., Rohde, C.: Almost Parallel Flows in Porous Media. In: Fuhrmann, J., Ohlberger, M., and Rohde, C. (eds.) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. pp. 873–881. Springer International Publishing (2014). https://doi.org/10.1007/978-3-319-05591-6_88.
    2. Bürger, R., Kröker, I., Rohde, C.: A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit. ZAMM Z. Angew. Math. Mech. 94, 793–817 (2014). https://doi.org/10.1002/zamm.201200174.
    3. Chalons, C., Engel, P., Rohde, C.: A Conservative and Convergent Scheme for Undercompressive Shock Waves. SIAM J. Numer. Anal. 52, 554–579 (2014).
    4. Corli, A., Rohde, C., Schleper, V.: Parabolic approximations of diffusive-dispersive equations. J. Math. Anal. Appl. 414, 773–798 (2014).
    5. Ehlers, W., Helmig, R., Rohde, C.: Editorial: Deformation and transport phenomena in porous media. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 94, 559--559 (2014). https://doi.org/10.1002/zamm.201400559.
    6. Engel, P., Viorel, A., Rohde, C.: A Low-Order Approximation for Viscous-Capillary Phase Transition  Dynamics. Port. Math. 70, 319–344 (2014).
    7. Fechter, S., Zeiler, C., Munz, C.-D., Rohde, C.: 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).
    8. Kabil, B., Rohde, C.: The influence of surface tension and configurational forces on the  stability of liquid-vapor interfaces. Nonlinear Analysis: Theory, Methods & Applications. 107, 63–75 (2014).
    9. Köppel, M., Kröker, I., Rohde, C.: Stochastic Modeling for Heterogeneous Two-Phase Flow. In: Fuhrmann, J., Ohlberger, M., and Rohde, C. (eds.) Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects. pp. 353–361. Springer International Publishing (2014). https://doi.org/10.1007/978-3-319-05684-5_34.
  12. 2013

    1. Eck, Ch., Kutter, M., Sändig, A.-M., Rohde, Ch.: 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. 93, 745--761 (2013). https://doi.org/10.1002/zamm.201200238.
    2. Eisenschmidt, K., Rauschenberger, P., Rohde, C., Weigand, B.: 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).
    3. Rohde, C., Wang, W., Xie, F.: Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation  hydrodynamics model: superposition of rarefaction and contact waves. Communications on Pure and Applied Analysis. 12, 2145--2171 (2013). https://doi.org/10.3934/cpaa.2013.12.2145.
    4. Rohde, C., Wang, W., Xie, F.: Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation  Hydrodynamics Model. Mathematical Models and Methods in Applied Sciences. 23, 441--469 (2013). https://doi.org/10.1142/S0218202512500522.
  13. 2012

    1. Chalons, C., Coquel, F., Engel, P., Rohde, C.: Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition  Problems. SIAM Journal on Scientific Computing. 34, A1753--A1776 (2012). https://doi.org/10.1137/110848815.
    2. Corli, A., Rohde, C.: Singular limits for a parabolic-elliptic regularization of scalar conservation laws. J. Differential Equations. 253, 1399--1421 (2012). https://doi.org/10.1016/j.jde.2012.05.006.
    3. Dreyer, W., Giesselmann, J., Kraus, C., Rohde, C.: Asymptotic Analysis for Korteweg Models. Interfaces Free Bound. 14, 105–143 (2012).
    4. Engel, P., Rohde, C.: On the Space-Time Expansion Discontinuous Galerkin Method. In: Li, T. and Jiang, S. (eds.) Hyperbolic Problems: Theory, Numerics and Applications. pp. 406--414 (2012).
    5. Jaegle, F., Rohde, C., Zeiler, C.: A multiscale method for compressible liquid-vapor flow with surface  tension. ESAIM: Proc. 38, 387–408 (2012). https://doi.org/10.1051/proc/201238022.
    6. Kissling, F., Helmig, R., Rohde, C.: Simulation of Infiltration Processes in the Unsaturated Zone  Using a Multi-Scale Approach. Vadose Zone J. 11, (2012). https://doi.org/10.2136/vzj2011.0193.
    7. Kissling, F., Rohde, C.: Numerical Simulation of Nonclassical Shock Waves in Porous  Media with a Heterogeneous Multiscale Method. In: Li, T. and Jiang, S. (eds.) Hyperbolic Problems: Theory, Numerics and Applications. pp. 469--478 (2012).
    8. Kröker, I., Rohde, C.: Finite volume schemes for hyperbolic balance laws with multiplicative  noise. Appl. Numer. Math. 62, 441--456 (2012). https://doi.org/10.1016/j.apnum.2011.01.011.
    9. Richter, T., Rudlof, S., Adjibadji, B., Bernlöhr, H., Gröninger, C., Munz, C.-D., Stock, A., Rohde, C., Helmig, R.: ViPLab: a virtual programming laboratory for mathematics and engineering. Interactive Technology and Smart Education. 9, 246–262 (2012). https://doi.org/10.1108/17415651211284039.
    10. Rohde, C., Xie, F.: Global existence and blowup phenomenon for a 1D radiation hydrodynamics  model problem. Math. Methods Appl. Sci. 35, 564--573 (2012). https://doi.org/10.1002/mma.1593.
  14. 2011

    1. Bürger, R., Kröker, I., Rohde, C.: Uncertainty quantification for a clarifier-thickener model with random  feed. In: Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2. pp. 195--203. Springer (2011). https://doi.org/10.1007/978-3-642-20671-9_21.
    2. Richter, Th., Rudlof, S., Adjibadji, B., Berlohr, H., Gruninger, Ch., Munz, C.-D., Rohde, Ch., Helmig, R.: ViPLab - A Virtual Programming Laboratory for Mathematics and Engineering. In: Proceedings of the 2011 IEEE International Symposium on Multimedia. pp. 537--542. IEEE Computer Society, Washington, DC, USA (2011). https://doi.org/10.1109/ISM.2011.95.
  15. 2010

    1. Kissling, F., Rohde, C.: The Computation of Nonclassical Shock Waves with a Heterogeneous  Multiscale Method. Netw. Heterog. Media. 5, 661--674 (2010). https://doi.org/10.3934/nhm.2010.5.661.
    2. Rohde, C.: A local and low-order Navier-Stokes-Korteweg system. In: Nonlinear partial differential equations and hyperbolic wave phenomena. pp. 315--337. Amer. Math. Soc., Providence, RI (2010). https://doi.org/10.1090/conm/526/10387.
  16. 2009

    1. Kissling, F., LeFloch, P.G., Rohde, C.: A Kinetic Decomposition for Singular Limits of non-local  Conservation Laws. J. Differential Equations. 247, 3338--3356 (2009). https://doi.org/10.1016/j.jde.2009.05.006.
  17. 2008

    1. Dressel, A., Rohde, C.: Global existence and uniqueness of solutions for a viscoelastic two-phase  model. Indiana Univ. Math. J. 57, 717--755 (2008). https://doi.org/10.1512/iumj.2008.57.3271.
    2. Dressel, A., Rohde, C.: A finite-volume approach to liquid-vapour fluids with phase transition. In: Finite volumes for complex applications V. pp. 53--68. ISTE, London (2008).
    3. Haink, J., Rohde, C.: Local discontinuous-Galerkin schemes for model problems in phase  transition theory. Commun. Comput. Phys. 4, 860–893 (2008).
    4. Rohde, C., Tiemann, N., Yong, W.-A.: Weak and classical solutions for a model problem in radiation hydrodynamics. In: Hyperbolic problems: theory, numerics, applications. pp. 891--899. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-75712-2_93.
    5. Rohde, C., Yong, W.-A.: Dissipative entropy and global smooth solutions in radiation hydrodynamics  and magnetohydrodynamics. Math. Models Methods Appl. Sci. 18, 2151--2174 (2008). https://doi.org/10.1142/S0218202508003327.
  18. 2007

    1. Merkle, C., Rohde, C.: The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. M2AN Math. Model. Numer. Anal. 41, 1089--1123 (2007). https://doi.org/10.1051/m2an:2007048.
    2. Rohde, C., Yong, W.-A.: The nonrelativistic limit in radiation hydrodynamics. I. Weak  entropy solutions for a model problem. J. Differential Equations. 234, 91--109 (2007). https://doi.org/10.1016/j.jde.2006.11.010.
  19. 2006

    1. Diehl, D., Rohde, C.: On the structure of MHD shock waves in diffusive-dispersive media. J. Math. Fluid Mech. 8, 120--145 (2006). https://doi.org/10.1007/s00021-004-0149-z.
    2. Haink, J., Rohde, C.: Phase transition in compressible media and nonlocal capillarity terms. In: Hyperbolic problems: theory, numerics and applications. I. pp. 147--154. Yokohama Publ., Yokohama (2006).
    3. Jovanović, V., Rohde, C.: Error estimates for finite volume approximations of classical solutions  for nonlinear systems of hyperbolic balance laws. SIAM J. Numer. Anal. 43, 2423--2449 (electronic) (2006). https://doi.org/10.1137/S0036142903438136.
    4. Merkle, C., Rohde, C.: Computation of dynamical phase transitions in solids. Appl. Numer. Math. 56, 1450--1463 (2006). https://doi.org/10.1016/j.apnum.2006.03.025.
  20. 2005

    1. Coquel, F., Diehl, D., Merkle, C., Rohde, C.: Sharp and diffuse interface methods for phase transition problems  in liquid-vapour flows. In: Numerical methods for hyperbolic and kinetic problems. pp. 239--270. Eur. Math. Soc., Zürich (2005). https://doi.org/10.4171/012-1/11.
    2. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: Radiation magnetohydrodynamics: analysis for model problems and efficient  3d-simulations for the full system. In: Analysis and numerics for conservation laws. pp. 163--202. Springer, Berlin (2005). https://doi.org/10.1007/3-540-27907-5_8.
    3. Gander, M.J., Rohde, C.: Nonlinear advection problems and overlapping Schwarz waveform relaxation. In: Domain decomposition methods in science and engineering. pp. 251--258. Springer, Berlin (2005). https://doi.org/10.1007/3-540-26825-1_23.
    4. Gander, M.J., Rohde, C.: Overlapping Schwarz waveform relaxation for convection-dominated  nonlinear conservation laws. SIAM J. Sci. Comput. 27, 415--439 (2005). https://doi.org/10.1137/030601090.
    5. Jovanović, V., Rohde, C.: Finite-volume schemes for Friedrichs systems in multiple space  dimensions: a priori and a posteriori error estimates. Numer. Methods Partial Differential Equations. 21, 104--131 (2005). https://doi.org/10.1002/num.20026.
    6. Rohde, C.: Scalar conservation laws with mixed local and nonlocal diffusion-dispersion  terms. SIAM J. Math. Anal. 37, 103--129 (electronic) (2005). https://doi.org/10.1137/S0036141004443300.
    7. Rohde, C.: Phase transitions and sharp-interface limits for the 1d-elasticity  system with non-local energy. Interfaces Free Bound. 7, 107--129 (2005). https://doi.org/10.4171/IFB/116.
    8. Rohde, C.: On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour  phase transitions. ZAMM Z. Angew. Math. Mech. 85, 839--857 (2005). https://doi.org/10.1002/zamm.200410211.
  21. 2004

    1. Dedner, A., Rohde, C.: Numerical approximation of entropy solutions for hyperbolic integro-differential  equations. Numer. Math. 97, 441--471 (2004). https://doi.org/10.1007/s00211-003-0502-9.
    2. Dedner, A., Rohde, C., Schupp, B., Wesenberg, M.: A parallel, load-balanced MHD code on locally-adapted unstructured  grids in 3d. Comput. Vis. Sci. 7, 79--96 (2004). https://doi.org/10.1007/s00791-004-0140-5.
    3. Rohde, C., Thanh, M.D.: Global existence for phase transition problems via a variational  scheme. J. Hyperbolic Differ. Equ. 1, 747--768 (2004). https://doi.org/10.1142/S0219891604000329.
  22. 2003

    1. Dedner, A., Kröner, D., Rohde, C., Schnitzer, T., Wesenberg, M.: 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. pp. 573--589. Springer, Berlin (2003).
    2. Dedner, A., Rohde, C., Wesenberg, M.: Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics. In: Hyperbolic problems: theory, numerics, applications. pp. 499--508. Springer, Berlin (2003).
    3. Dedner, A., Rohde, C., Wesenberg, M.: A new approach to divergence cleaning in magnetohydrodynamic simulations. In: Hyperbolic problems: theory, numerics, applications. pp. 509--518. Springer, Berlin (2003).
    4. Freistühler, H., Rohde, C.: The bifurcation analysis of the MHD Rankine-Hugoniot equations for a perfect gas. Phys. D. 185, 78--96 (2003). https://doi.org/10.1016/S0167-2789(03)00206-9.
    5. Kröner, D., Küther, M., Ohlberger, M., Rohde, C.: A posteriori error estimates and adaptive methods for hyperbolic  and convection dominated parabolic conservation laws. In: Trends in nonlinear analysis. pp. 289--306. Springer, Berlin (2003).
    6. Rohde, C., Zajaczkowski, W.: On the Cauchy problem for the equations of ideal compressible MHD  fluids with radiation. Appl. Math. 48, 257--277 (2003). https://doi.org/10.1023/A:1026010631074.
  23. 2002

    1. Dedner, A., Rohde, C.: FV-schemes for a scalar model problem of radiation magnetohydrodynamics. In: Finite volumes for complex applications, III (Porquerolles, 2002). pp. 165--172. Hermes Sci. Publ., Paris (2002).
    2. Freistühler, H., Rohde, C.: Numerical computation of viscous profiles for hyperbolic conservation  laws. Math. Comp. 71, 1021--1042 (electronic) (2002). https://doi.org/10.1090/S0025-5718-01-01340-0.
    3. Lefloch, P.G., Mercier, J.M., Rohde, C.: Fully discrete, entropy conservative schemes of arbitrary order. SIAM J. Numer. Anal. 40, 1968--1992 (electronic) (2002). https://doi.org/10.1137/S003614290240069X.
    4. Ohlberger, M., Rohde, C.: Adaptive finite volume approximations for weakly coupled convection  dominated parabolic systems. IMA J. Numer. Anal. 22, 253--280 (2002). https://doi.org/10.1093/imanum/22.2.253.
  24. 2001

    1. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: Godunov-type schemes for the MHD equations. In: Godunov methods (Oxford, 1999). pp. 209--216. Kluwer/Plenum, New York (2001).
    2. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: MHD instabilities arising in solar physics: a numerical approach. In: Hyperbolic problems: theory, numerics, applications, Vol. I,  II (Magdeburg, 2000). pp. 277--286. Birkhäuser, Basel (2001).
    3. Freistühler, H., Fries, C., Rohde, C.: Existence, bifurcation, and stability of profiles for classical and  non-classical shock waves. In: Ergodic theory, analysis, and efficient simulation of dynamical systems. pp. 287--309, 814. Springer, Berlin (2001).
    4. Freistühler, H., Rohde, C.: A numerical study on viscous profiles of MHD shock waves. In: Hyperbolic problems: theory, numerics, applications, Vol. I,  II (Magdeburg, 2000). pp. 399--408. Birkhäuser, Basel (2001).
    5. Haasdonk, B., Kröner, D., Rohde, C.: Convergence of a staggered Lax-Friedrichs scheme for nonlinear  conservation laws on unstructured two-dimensional grids. Numer. Math. 88, 459--484 (2001). https://doi.org/10.1007/s211-001-8011-x.
    6. Haasdonk, B., Kröner, D., Rohde, C.: Convergence of a staggered Lax-Friedrichs scheme for nonlinear  conservation laws on unstructured two-dimensional grids. Numer. Math. 88, 459--484 (2001). https://doi.org/10.1007/s211-001-8011-x.
    7. Hillen, T., Rohde, C., Lutscher, F.: Existence of weak solutions for a hyperbolic model of chemosensitive  movement. J. Math. Anal. Appl. 260, 173--199 (2001). https://doi.org/10.1006/jmaa.2001.7447.
    8. LeFloch, P.G., Rohde, C.: Zero diffusion-dispersion limits for self-similar Riemann solutions  to hyperbolic systems of conservation laws. Indiana Univ. Math. J. 50, 1707--1743 (2001). https://doi.org/10.1512/iumj.2001.50.2057.
  25. 2000

    1. Lefloch, P.G., Rohde, C.: High-order schemes, entropy inequalities, and nonclassical shocks. SIAM J. Numer. Anal. 37, 2023--2060 (electronic) (2000). https://doi.org/10.1137/S0036142998345256.
  26. 1999

    1. Dedner, A., Rohde, C., Wesenberg, M.: A MHD-simulation in solar physics. In: Finite volumes for complex applications II. pp. 491--498. Hermes Sci. Publ., Paris (1999).
    2. Freistühler, H., Rohde, C.: Numerical methods for viscous profiles of non-classical shock waves. In: Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich,  1998). pp. 333--342. Birkhäuser, Basel (1999).
  27. 1998

    1. Rohde, C.: Entropy solutions for weakly coupled hyperbolic systems in several  space dimensions. Z. Angew. Math. Phys. 49, 470--499 (1998). https://doi.org/10.1007/s000000050102.
    2. Rohde, C.: Upwind finite volume schemes for weakly coupled hyperbolic systems  of conservation laws in 2D. Numer. Math. 81, 85--123 (1998). https://doi.org/10.1007/s002110050385.
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