Publications

List of publications of the Chair of Applied Mathematics.

  1. 2024

    1. M. Hörl and C. Rohde, “Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture,” Netw. Heterog. Media, vol. 19, no. 1, Art. no. 1, 2024, doi: 10.3934/nhm.2024006.
    2. T. Mel’nyk and C. Rohde, “Asymptotic expansion for convection-dominated transport in a thin graph-like junction,” Analysis and Applications (accepted) (see also arXiv e-prints), 2024. doi: 10.48550/ARXIV.2208.05812.
    3. T. Mel’nyk and C. Rohde, “Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks,” J. Math. Anal. Appl., vol. 529, no. 1, Art. no. 1, 2024, doi: 10.1016/j.jmaa.2023.127587.
    4. T. Mel’nyk and C. Rohde, “Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: strong boundary interactions,” Asymptotic Analysis, vol. 136, 2024, doi: 10.3233/ASY-231876.
    5. L. Ruan and I. Rybak, “Stokes-Brinkman-Darcy models for coupled fluid-porous systems: derivation, analysis and validation,” Appl. Math. Comp.  (submitted), 2024.
  2. 2023

    1. M. Alkämper, J. Magiera, and C. Rohde, “An Interface Preserving Moving Mesh in Multiple Space Dimensions,” accepted by ACM Trans. Math. Softw., vol. abs/2112.11956, 2023, doi: https://dl.acm.org/doi/10.1145/3630000.
    2. 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.
    3. S. Burbulla, M. Hörl, and C. Rohde, “Flow in Porous Media with Fractures of Varying Aperture,” SIAM J. Sci. Comput, vol. 45, no. 4, Art. no. 4, 2023, doi: 10.1137/22M1510406.
    4. E. Eggenweiler, J. Nickl, and I. Rybak, “Justification of generalized interface conditions for Stokes-Darcy problems,” in Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems, E. Franck, J. Fuhrmann, V. Michel-Dansac, and L. Navoret, Eds., in Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems. Springer Nature Switzerland, 2023, pp. 275–283. doi: 10.1007/978-3-031-40864-9_22.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. I. Kröker, S. Oladyshkin, and I. Rybak, “Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems,” Comput. Geosci., 2023, doi: 10.1007/s10596-023-10236-z.
    10. J. Magiera and C. Rohde, “A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate,” Accepted by Comm. App  Math. Comp., 2023, doi: https://arxiv.org/abs/2309.00876.
    11. 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
    12. C. T. Miller, W. G. Gray, C. E. Kees, I. Rybak, and B. J. Shepherd, “Correction to: Modelling Sediment Transport in Three-Phase Surface Water Systems,” J. Hydraul. Res., vol. 61, pp. 168–171, 2023, doi: 10.1080/00221686.2022.2107580.
    13. F. Mohammadi et al., “A Surrogate-Assisted Uncertainty-Aware Bayesian Validation Framework and its Application to Coupling Free Flow and Porous-Medium Flow,” Comput. Geosci., 2023, doi: 10.1007/s10596-023-10228-z.
    14. L. Ruan and I. Rybak, “Stokes-Brinkman-Darcy models for coupled free-flow and porous-medium systems,” in Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems, E. Franck, J. Fuhrmann, V. Michel-Dansac, and L. Navoret, Eds., in Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems. Springer Nature Switzerland, 2023, pp. 365–373. doi: 10.1007/978-3-031-40864-9_31.
    15. 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.
    16. P. Strohbeck, E. Eggenweiler, and I. Rybak, “A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface,” Transp. Porous Med., vol. 147, no. 3, Art. no. 3, Apr. 2023, doi: 10.1007/s11242-023-01919-3.
    17. P. Strohbeck, C. Riethmüller, D. Göddeke, and I. Rybak, “Robust and efficient preconditioners for Stokes-Darcy problems,” in Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems, E. Franck, J. Fuhrmann, V. Michel-Dansac, and L. Navoret, Eds., in Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems. Springer Nature Switzerland, 2023, pp. 375–383. doi: 10.1007/978-3-031-40864-9_32.
  3. 2022

    1. 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.
    2. 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.
    3. E. Eggenweiler, M. Discacciati, and I. Rybak, “Analysis of the Stokes-Darcy problem with generalised interface conditions,” ESAIM Math. Model. Numer. Anal., vol. 56, pp. 727–742, 2022, doi: 10.1051/m2an/2022025.
    4. E. Eggenweiler, “Interface conditions for arbitrary flows in Stokes-Darcy systems : derivation, analysis and validation.” Universität Stuttgart, 2022. doi: 10.18419/OPUS-12573.
    5. G. C. Hsiao, T. Sánchez-Vizuet, and W. L. Wendland, “A Boundary-Field Formulation for Elastodynamic Scattering,” Journal of Elasticity, 2022, doi: https://doi.org/10.1007/s10659-022-09964-7.
    6. M. Kohr, S. E. Mikhailov, and W. L. Wendland, “On some mixed-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces,” JMAA, vol. 516, no. 1, 126464, Art. no. 1, 126464, 2022, [Online]. Available: https://doi.org/10.1016/j.jmaa.2022.126464
    7. M. Kohr, S. E. Mikhailov, and W. L. Wendland, “Non-homogeneous Dirichlet-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces,” Calc. Var. Partial Differential Equations, vol. 61, p. Paper No. 198 (2022) 47 pp., 2022.
    8. 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.
    9. 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.
    10. L. von Wolff and I. S. Pop, “Upscaling of a Cahn–Hilliard Navier–Stokes model with precipitation and dissolution in a thin strip,” Journal of Fluid Mechanics, vol. 941, pp. A49--, 2022, doi: DOI: 10.1017/jfm.2022.308.
  4. 2021

    1. 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.
    2. 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.
    3. 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.
    4. E. Eggenweiler and I. Rybak, “Effective coupling conditions for arbitrary flows in Stokes-Darcy systems,” Multiscale Model. Simul., vol. 19, pp. 731–757, 2021, doi: 10.1137/20M1346638.
    5. 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
    6. 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.
    7. G. C. Hsiao and W. L. Wendland, “On the propagation of acoustic waves in a thermo-electro-magneto-elastic solid,” Applicable Analysis, vol. 101 (2022), no. 0, Art. no. 0, 2021, doi: 10.1080/00036811.2021.1986027.
    8. M. Kohr, S. E. Mikhailov, and W. L. Wendland, “Layer potential theory for the anisotropic Stokes system with variable L∞ symmetrically elliptic tensor coeffici,” Math. Methods Appl. Sci., vol. 44, no. 12, Art. no. 12, 2021, doi: 10.1002/mma.7167.
    9. J. Magiera, “A Molecular--Continuum Multiscale Solver for Liquid--Vapor Flow,” in Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting), in Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting), vol. 41. 2021. doi: 10.14760/OWR-2021-41.
    10. J. Magiera, “A Molecular--Continuum Multiscale Solver for Liquid--Vapor Flow: Modeling and Numerical Simulation,” Ph.D. Thesis, 2021. doi: 10.18419/opus-11797.
    11. 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.
    12. 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.
    13. 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.
    14. I. Rybak, C. Schwarzmeier, E. Eggenweiler, and U. Rüde, “Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models,” Comput. Geosci., vol. 25, pp. 621–635, 2021, doi: 10.1007/s10596-020-09994-x.
    15. L. von Wolff, “The Dune-Phasefield Module release 1.0,” DaRUS, 2021, doi: 10.18419/darus-1634.
    16. 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.
    17. A. Wagner et al., “Permeability estimation of regular porous structures: a benchmark for comparison of methods,” Transp. Porous Med., vol. 138, pp. 1–23, 2021, doi: 10.1007/s11242-021-01586-2.
  5. 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. 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.
    3. I. Berre et al., “Verification benchmarks for single-phase flow in three-dimensional fractured porous media.” 2020.
    4. C. Bringedal, L. Von Wolff, and I. S. Pop, “Phase Field Modeling of Precipitation and Dissolution Processes in Porous Media: Upscaling and Numerical Experiments,” Multiscale Modeling &amp$\mathsemicolon$ Simulation, vol. 18, no. 2, Art. no. 2, Jan. 2020, doi: 10.1137/19m1239003.
    5. 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.
    6. E. Eggenweiler and I. Rybak, “Unsuitability of the Beavers-Joseph interface condition for filtration problems,” J. Fluid Mech., vol. 892, p. A10, 2020, doi: http://dx.doi.org/10.1017/jfm.2020.194.
    7. E. Eggenweiler and I. Rybak, “Interface conditions for arbitrary flows in coupled porous-medium and free-flow systems,” in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F. Radu, and J. Fuhrmann, Eds., in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, vol. 323. Springer International Publishing, 2020, pp. 345--353. doi: 10.1007/978-3-030-43651-3_31.
    8. J. T. Gerstenberger, S. Burbulla, and D. Kröner, “Discontinuous Galerkin method for incompressible two-phase flows,” Submitted to: Springer Proceedings in Mathematics & Statistics, 2020.
    9. 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
    10. 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
    11. 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.
    12. D. Göddeke, M. Schirwon, and N. Borg, “Smartphone-Apps im Mathematikstudium,” 2020, doi: 10.18419/darus-1147.
    13. 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.
    14. T. Koch et al., “DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling,” Computers & Mathematics with Applications, 2020, doi: https://doi.org/10.1016/j.camwa.2020.02.012.
    15. M. Kohr, S. E. Mikhailov, and W. L. Wendland, “Potentials and transmission problems in weighted Sobolev spaces for anisotropic Stokes and Navier–Stokes systems with L∞ strongly elliptic coefficient tensor,” Complex Variables and Elliptic Equations, vol. 65, no. 1, Art. no. 1, 2020, doi: 10.1080/17476933.2019.1631293.
    16. 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.
    17. 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
    18. L. Ostrowski and C. Rohde, “Compressible multicomponent flow in porous media with Maxwell-Stefan diffusion,” Math. Meth. Appl. Sci., vol. 43, no. 7, Art. no. 7, 2020, doi: 10.1002/mma.6185.
    19. 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
    20. 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.
    21. I. Rybak and S. Metzger, “A dimensionally reduced Stokes-Darcy model for fluid flow in fractured porous media,” Appl. Math. Comp., vol. 384, 2020, doi: 10.1016/j.amc.2020.125260.
  6. 2019

    1. 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.
    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. M. Kohr, S. E. Mikhailov, and W. L. Wendland, “Newtonian and Single Layer Potentials for the Stokes System with L∞ Coefficients and the Exterior Dirichlet Problem,” in Analysis as a Life: Dedicated to Heinrich Begehr on the Occasion of his 80th Birthday, S. Rogosin and A. O. Celebi, Eds., in Analysis as a Life: Dedicated to Heinrich Begehr on the Occasion of his 80th Birthday. , Cham: Springer International Publishing, 2019, pp. 237--260. doi: 10.1007/978-3-030-02650-9_12.
    4. M. Kohr and W. L. Wendland, “Boundary value problems for the Brinkman system with L∞ coefficients in Lipschitz domains on compact Riemannian manifolds. A variational approach,” Journal de Mathématiques Pures et Appliquées, no. 131, Art. no. 131, Nov. 2019, doi: https://doi.org/10.1016/j.matpur.2019.04.002.
    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. 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.
    7. C. T. Miller, W. G. Gray, C. E. Kees, I. V. Rybak, and B. J. Shepherd, “Modeling sediment transport in three-phase surface water systems,” J. Hydraul. Res., vol. 57, 2019, doi: 10.1080/00221686.2019.1581673.
    8. L. Ostrowski and F. Massa, “An incompressible-compressible approach for droplet impact,” in Proceedings of the DIPSI Workshop 2019: Droplet ImpactPhenomena & Spray Investigations, Bergamo, Italy, 17th May 2019, G. Cossali and S. Tonini, Eds., in Proceedings of the DIPSI Workshop 2019: Droplet ImpactPhenomena & Spray Investigations, Bergamo, Italy, 17th May 2019. Università degli studi di Bergamo, 2019, pp. 18–21. doi: 10.6092/DIPSI2019_pp18-21.
    9. D. Seus, F. A. Radu, and C. Rohde, “A linear domain decomposition method for two-phase flow in porous media,” in Numerical Mathematics and Advanced Applications ENUMATH 2017, in Numerical Mathematics and Advanced Applications ENUMATH 2017. Springer International Publishing, 2019, pp. 603–614. doi: 10.1007/978-3-319-96415-7_55.
    10. 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.
  7. 2018

    1. J. Dürrwächter, T. Kuhn, F. Meyer, L. Schlachter, and F. Schneider, “A hyperbolicity-preserving discontinuous stochastic Galerkin scheme  for uncertain hyperbolic systems of equations,” Journal of Computational and Applied Mathematics, p. 112602, 2018, doi: https://doi.org/10.1016/j.cam.2019.112602.
    2. 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.
    3. J. Giesselmann, N. Kolbe, M. Lukacova-Medvidova, and N. Sfakianakis, “Existence and uniqueness of global classical solutions to a two species  cancer invasion haptotaxis model,” Accepted for publication in Discrete Contin. Dyn. Syst. Ser. B., 2018, [Online]. Available: https://arxiv.org/abs/1704.08208
    4. H. Gimperlein, F. Meyer, C. Özdemir, D. Stark, and E. P. Stephan, “Boundary elements with mesh refinements for the wave equation.,” Numer. Math., vol. 139, no. 4, Art. no. 4, Aug. 2018, doi: https://doi.org/10.1007/s00211-018-0954-6.
    5. H. Gimperlein, F. Meyer, C. Özdemir, and E. P. Stephan, “Time domain boundary elements for dynamic contact problems,” Computer Methods in Applied Mechanics and Engineering, vol. 333, pp. 147–175, 2018, doi: https://doi.org/10.1016/j.cma.2018.01.025.
    6. H. Harbrecht, W. L. Wendland, and N. Zorii, “Minimal energy problems for strongly singular Riesz kernels,” Math. Nachr., no. 291, Art. no. 291, 2018, doi: https://doi.org/10.1002/mana.201600024.
    7. G. C. Hsiao, O. Steinbach, and W. L. Wendland, “Boundary Element Methods: Foundation and Error Analysis,” vol. Encyclopedia of Computational Mechanics Second Edition, p. 62, 2018, doi: https://doi.org/10.1002/9781119176817.ecm2007.
    8. M. Kohr and W. L. Wendland, “Variational approach for the Stokes and Navier–Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds,” Calculus of Variations and Partial Differential Equations, p. 57:165, 2018, doi: https://doi.org/10.1007/s00526-018-1426-7.
    9. M. Kohr and W. L. Wendland, “Layer Potentials and Poisson Problems for the Nonsmooth Coefficient Brinkman System in Sobolev and Besov Spaces,” Journal of Mathematical Fluid Mechanics, vol. 4, no. 20, Art. no. 20, 2018, doi: https://doi.org/10.1007/s00021-018-0394-1.
    10. 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.
    11. 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
    12. 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.
    13. 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.
    14. 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.
  8. 2017

    1. 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.
    2. 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.
    3. S. Funke, T. Mendel, A. Miller, S. Storandt, and M. Wiebe, “Map Simplification with Topology Constraints: Exactly and in Practice,” in Proceedings of the Ninteenth Workshop on Algorithm Engineering and  Experiments, ALENEX 2017, Barcelona, Spain, Hotel Porta Fira, January  17-18, 2017., in Proceedings of the Ninteenth Workshop on Algorithm Engineering and  Experiments, ALENEX 2017, Barcelona, Spain, Hotel Porta Fira, January  17-18, 2017. 2017, pp. 185--196. doi: 10.1137/1.9781611974768.15.
    4. J. Giesselmann, C. Lattanzio, and A. E. Tzavaras, “Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics,” ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 223, no. 3, Art. no. 3, Mar. 2017, doi: 10.1007/s00205-016-1063-2.
    5. J. Giesselmann and T. Pryer, “Goal-oriented error analysis of a DG scheme for a second gradient  elastodynamics model,” in Finite Volumes for Complex Applications VIII-Methods and Theoretical  Aspects, C. Cances and P. Omnes, Eds., in Finite Volumes for Complex Applications VIII-Methods and Theoretical  Aspects, vol. 199. 2017. [Online]. Available: http://www.springer.com/de/book/9783319573960
    6. J. Giesselmann and T. Pryer, “A posteriori analysis for dynamic model adaptation in convection-dominated problems,” MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, vol. 27, no. 13, Art. no. 13, Dec. 2017, doi: 10.1142/S0218202517500476.
    7. J. Giesselmann and A. E. Tzavaras, “Stability properties of the Euler-Korteweg system with nonmonotone pressures,” APPLICABLE ANALYSIS, vol. 96, no. 9, SI, Art. no. 9, SI, 2017, doi: 10.1080/00036811.2016.1276175.
    8. R. Gutt, M. Kohr, S. Mikhailov, and W. L. Wendland, “On the mixed problem for the semilinear Darcy-Forchheimer-Brinkman  systems in Besov spaces on creased Lipschitz domains,” Math. Meth. Appl. Sci., vol. 18, pp. 7780–7829, 2017, doi: 10.1002/mma.4562.
    9. R. Gutt, M. Kohr, S. E. Mikhailov, and W. L. Wendland, “On the mixed problem for the semilinear Darcy-Forchheimer-Brinkman PDE system in Besov spaces on creased Lipschitz domains,” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol. 40, no. 18, Art. no. 18, Dec. 2017, doi: 10.1002/mma.4562.
    10. H. Harbrecht, W. L. Wendland, and N. Zorii, “Riesz energy problems for strongly singular kernels,” Math. Nachr., 2017, doi: 10.1002/mana.201600024.
    11. M. Kohr, D. Medkova, and W. L. Wendland, “On the Oseen-Brinkman flow around an (m-1)-dimensional obstacle,” Monatshefte für Mathematik, vol. 483, pp. 269–302, 2017, doi: MOFM-D16-00078.
    12. M. Kohr, S. Mikhailov, and W. L. Wendland, “Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman  systems in Lipschitz domains on compact Riemannian mani,” J of Mathematical Fluid Mechanics, vol. 19, pp. 203–238, 2017.
    13. 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.
    14. 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
    15. M. Köppel et al., “Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage.” Nov. 2017. doi: 10.5281/zenodo.933827.
    16. 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.
    17. V. Maz’ya, D. Natroshvili, E. Shargorodsky, and W. L. Wendland, Eds., Recent Trends in Operator Theory and Partial Differential Equations.  The Roland Duduchava Anniverary Volume, no. 258. Birkhäuser/Springer International, 2017.
  9. 2016

    1. 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.
    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. 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.
    4. A. Dedner and J. Giesselmann, “A posteriori analysis of fully discrete method of lines DG schemes  for systems of conservation laws,” SIAM J. Numer. Anal., vol. 54, no. 6, Art. no. 6, 2016, [Online]. Available: http://epubs.siam.org/toc/sjnaam/54/6
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. J. Giesselmann, “Relative entropy based error estimates for discontinuous Galerkin  schemes,” Bull. Braz. Math. Soc. (N.S.), vol. 47, no. 1, Art. no. 1, 2016, doi: 10.1007/s00574-016-0144-z.
    11. J. Giesselmann and P. G. LeFloch, “Formulation and convergence of the finite volume method for conservation  laws on spacetimes with boundary,” ArXiv, 2016. [Online]. Available: http://arxiv.org/abs/1607.03944
    12. J. Giesselmann and T. Pryer, “Reduced relative entropy techniques for a posteriori analysis of  multiphase problems in elastodynamics,” IMA J. Numer. Anal., vol. 36, no. 4, Art. no. 4, 2016, [Online]. Available: http://imajna.oxfordjournals.org/content/36/4/1685
    13. J. Giesselmann and T. Pryer, “Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics,” BIT Numerical Mathematics, vol. 56, pp. 99-- 127, 2016, doi: 10.1007/s10543-015-0560-2.
    14. J. Gisselmann and T. Pryer, “Reduced relative entropy techniques for a posteriori analysis of    multiphase problems in elastodynamics,” IMA JOURNAL OF NUMERICAL ANALYSIS, vol. 36, no. 4, Art. no. 4, Oct. 2016, doi: 10.1093/imanum/drv052.
    15. R. Gutt, M. Kohr, C. Pintea, and W. L. Wendland, “On the transmission problems for the Oseen and Brinkman systems on  Lipschitz domains in compact Riemannian manifolds,” Math. Nachr, vol. 289, pp. 471–484, 2016.
    16. H. Harbrecht, W. L. Wendland, and N. Zorii, “Rapid solution of minimal Riesz energy problems,” Numer. Methods Partial Diff. Equ., vol. 32, pp. 1535–1552, 2016.
    17. 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.
    18. M. Kohr, L. de Cristoforis, S. Mikhailov, and W. L. Wendland, “Integral potential method for transmission problem with Lipschitz interface in R3 for the Stokes and Darcy-Forchheimer-Brinkman PED systems,” ZAMP, vol. 67:116, pp. 1–30, 2016.
    19. M. Kohr, M. Lanza de Cristoforis, and W. L. Wendland, “On the Robin transmission boundary value problem for the nonlinear  Darcy-Forchheimer-Brinkman and Navier-Stokes system,” J. Math. Fluid Mechanics, vol. 18, pp. 293–329, 2016.
    20. M. Kohr, S. E. Mikhailov, and W. L. Wendland, “Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman  systems in Lipschitz domains on compact Riemannian manifolds,” Journal of Mathematical Fluid Dynamics, vol. DOI 10.1007/s 00021-16-0273-6, 2016.
    21. M. Kohr, C. Pintea, and W. L. Wendland, “Poisson transmission problems for L^infty perturbations of the Stokes  system on Lipschitz domains on compact Riemannian manifolds,” J. Dyn. Diff. Equations, vol. DOI 110.1007/s10884-014-9359-0, 2016.
    22. M. Kohr, M. L. de Cristoforis, and W. L. Wendland, “On the Robin-Transmission Boundary Value Problems for the Nonlinear    Darcy-Forchheimer-Brinkman and Navier-Stokes Systems,” JOURNAL OF MATHEMATICAL FLUID MECHANICS, vol. 18, no. 2, Art. no. 2, Jun. 2016, doi: 10.1007/s00021-015-0236-3.
    23. 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.
    24. 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.
    25. L. Ostrowski, B. Ziegler, and G. Rauhut, “Tensor decomposition in potential energy surface representations,” The Journal of Chemical Physics, vol. 145, no. 10, Art. no. 10, 2016, doi: 10.1063/1.4962368.
    26. 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.
    27. I. Rybak and J. Magiera, “Decoupled schemes for free flow and porous medium systems,” in Domain Decomposition Methods in Science and Engineering XXII, T. D. et al., Ed., in Domain Decomposition Methods in Science and Engineering XXII, vol. 104. Springer, 2016, pp. 613--621. doi: 10.1007/978-3-319-18827-0\_54.
    28. 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, Art. no. 4, 2016, doi: 10.1007/s00033-016-0699-y.
    29. A. Stein, “Exakte Simulation von Optionspreisen und Sensitivitäten unter  stochastischer Volatilität,” Master Thesis, Germany, 2016.
  10. 2015

    1. J. Giesselmann, “Low Mach asymptotic preserving scheme for the Euler-Korteweg model,” IMA J. Numer. Anal., vol. 35, no. 2, Art. no. 2, 2015, doi: 10.1093/imanum/dru022.
    2. J. Giesselmann, “Relative entropy in multi-phase models of 1d elastodynamics: Convergence    of a non-local to a local model,” JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 258, no. 10, Art. no. 10, May 2015, doi: 10.1016/j.jde.2015.01.047.
    3. J. Giesselmann, “Entropy as a fundamental principle in hyperbolic conservation laws and related models,” Habilitationsschrift, Stuttgart, 2015.
    4. J. Giesselmann, C. Makridakis, and T. Pryer, “A posteriori analysis of discontinuous Galerkin schemes for systems  of hyperbolic conservation laws,” SIAM J. Numer. Anal., vol. 53, pp. 1280--1303, 2015, [Online]. Available: http://dx.doi.org/10.1137/140970999
    5. J. Giesselmann and T. Pryer, “ENERGY CONSISTENT DISCONTINUOUS GALERKIN METHODS FOR A    QUASI-INCOMPRESSIBLE DIFFUSE TWO PHASE FLOW MODEL,” ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION    MATHEMATIQUE ET ANALYSE NUMERIQUE, vol. 49, no. 1, Art. no. 1, Jan. 2015, doi: 10.1051/m2an/2014033.
    6. T. Grosan, M. Kohr, and W. L. Wendland, “Dirichlet problem for a nonlinear generalized Darcy-Forchheimer-Brinkman  system in Lipschitz domains,” Math. Meth. Appl. Sciences, vol. 38, pp. 3615–3628, 2015, doi: 10.1002/mma3302.
    7. 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, doi: 10.1137/120899236.
    8. M. Kohr, M. Lanza de Cristoforis, and W. L. Wendland, “Poisson problems for semilinear Brinkman systems on Lipschitz domains  in R^3,” ZAMP, vol. 66, pp. 833–846, 2015.
    9. M. Kohr, M. L. de Cristoforis, and W. L. Wendland, “Poisson problems for semilinear Brinkman systems on Lipschitz domains in    R-n,” ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, vol. 66, no. 3, Art. no. 3, Jun. 2015, doi: 10.1007/s00033-014-0439-0.
    10. M. Kohr, C. Pintea, and W. L. Wendland, “Poisson-Transmission Problems for -Perturbations of the Stokes System on    Lipschitz Domains in Compact Riemannian Manifolds,” JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, vol. 27, no. 3–4, Art. no. 3–4, Dec. 2015, doi: 10.1007/s10884-014-9359-0.
    11. 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.
    12. 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.
    13. S. Micula and W. L. Wendland, “Trigonometric collocation for nonlinear Riemann-Hilbert problems  in doubly connected domains,” IMA J. Num. Analysis, vol. 35, pp. 834–858, 2015.
    14. S. Micula and W. L. Wendland, “Trigonometric collocation for nonlinear Riemann-Hilbert problems on    doubly connected domains,” IMA JOURNAL OF NUMERICAL ANALYSIS, vol. 35, no. 2, Art. no. 2, Apr. 2015, doi: 10.1093/imanum/dru009.
    15. 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.
    16. 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.
    17. 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, doi: 10.1016/j.apnum.2014.05.001.
    18. I. V. Rybak, W. G. Gray, and C. T. Miller, “Modeling two-fluid-phase flow and species transport in porous media,” J. Hydrology, vol. 521, pp. 565--581, 2015, doi: https://doi.org/10.1016/j.jhydrol.2014.11.051.
    19. 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.
  11. 2014

    1. G. L. Aki, W. Dreyer, J. Giesselmann, and C. Kraus, “A quasi-incompressible diffuse interface model with phase transition,” Math. Models Methods Appl. Sci., vol. 24, no. 5, Art. no. 5, 2014, doi: 10.1142/S0218202513500693.
    2. 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., 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.
    3. 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.
    4. 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
    5. 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
    6. W. Dreyer, J. Giesselmann, and C. Kraus, “A compressible mixture model with phase transition,” Physica D, vol. 273–274, pp. 1–13, 2014, doi: http://dx.doi.org/10.1016/j.physd.2014.01.006.
    7. W. Dreyer, J. Giesselmann, and C. Kraus, “Modeling of compressible electrolytes with phase transition,” 2014. [Online]. Available: http://arxiv.org/abs/1405.6625
    8. 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.
    9. 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
    10. 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.
    11. J. Fuhrmann, M. Ohlberger, and C. Rohde, Eds., Finite Volumes for Complex Applications VII Elliptic, Parabolic and  Hyperbolic Problems, FVCA 7, Berlin, June 2014, vol. Vol. 77/78. in Springer Proceedings in Mathematics & Statistics, vol. Vol. 77/78. 2014.
    12. J. Giesselmann, “A Relative Entropy Approach to Convergence of a Low Order Approximation  to a Nonlinear Elasticity Model with Viscosity and Capillarity,” SIAM J. Math. Anal., vol. 46, no. 5, Art. no. 5, 2014, doi: 10.1137/140951710.
    13. J. Giesselmann, C. Makridakis, and T. Pryer, “Energy consistent DG methods for the Navier-Stokes-Korteweg system,” Math. Comp., vol. 83, pp. 2071-- 2099, 2014, doi: http://dx.doi.org/10.1090/S0025-5718-2014-02792-0.
    14. J. Giesselmann and T. M�ller, “Geometric error of finite volume schemes for conservation laws on  evolving surfaces,” Numer. Math., vol. 128, no. 3, Art. no. 3, 2014, doi: 10.1007/s00211-014-0621-5.
    15. J. Giesselmann and T. M�ller, “Estimating the Geometric Error of Finite Volume Schemes for Conservation  Laws on Surfaces for generic numerical flux functions,” in Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects, M. O. J. Fuhrmann and C. Rohde, Eds., in Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects, vol. 77. 2014.
    16. J. Giesselmann and T. Pryer, “On aposteriori error analysis of DG schemes approximating hyperbolic  conservation laws,” in Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects, M. O. J. Fuhrmann and C. Rohde, Eds., in Finite Volumes for Complex Applications VII-Methods and Theoretical  Aspects, vol. 77. 2014.
    17. J. Giesselmann and A. E. Tzavaras, “Singular Limiting Induced from Continuum Solutions and the Problem  of Dynamic Cavitation,” Arch. Ration. Mech. Anal., vol. 212, no. 1, Art. no. 1, 2014, doi: 10.1007/s00205-013-0677-x.
    18. J. Giesselmann and A. E. Tzavaras, “On cavitation in elastodynamics,” in Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona, A. Bressan, P. Marcati, and A. Marson, Eds., in Hyperbolic Problems: Theory, Numerics, Applications. AIMS, 2014, pp. 599–606. [Online]. Available: https://aimsciences.org/books/am/AMVol8.html
    19. H. Harbrecht, W. L. Wendland, and N. Zorii, “Riesz minimal energy problems on C^k-1,1 manifolds,” Math. Nachr., vol. 287, pp. 48–69, 2014.
    20. 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
    21. M. Kohr, M. Lanza de Cristoforis, and W. L. Wendland, “Nonlinear Darcy-Forchheimer-Brinkman system with linear boundary  conditions in Lipschitz domains,” in Complex Analysis and Potential Theory with Applications, A. G. T. Aliev Azerogly and S. V. Rogosin, Eds., in Complex Analysis and Potential Theory with Applications. , Cambridge Sci. Publ., 2014, pp. 111–124.
    22. M. Kohr, M. Lanza de Cristoforis, and W. L. Wendland, “Boundary value problems of Robin type for the Brinkman and Darcy-Forchheimer-Brinkman  systems in Lipschitz domains,” J. Math. Fluid Mechanics, vol. 16, pp. 595–830, 2014.
    23. M. Kohr, C. Pintea, and W. L. Wendland, “Neumann-transmission problems for pseudodifferential Brinkman operators  on Lipschitz domains in compact Riemannian manifolds,” Communications in Pure and Applied Analysis, vol. 13, pp. 1–28, 2014, doi: 03934/cpaa.2013.13.
    24. 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, vol. 77, 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.
    25. I. Rybak, “Coupling free flow and porous medium flow systems using sharp interface  and transition region concepts,” in Finite Volumes for Complex Applications VII - Elliptic, Parabolic and Hyperbolic Problems, FVCA 7, J. Fuhrmann, M. Ohlberger, and C. Rohde, Eds., in Finite Volumes for Complex Applications VII - Elliptic, Parabolic and Hyperbolic Problems, FVCA 7, vol. 78. Springer, Jun. 2014, pp. 703--711. doi: 10.1007/978-3-319-05591-6_70.
    26. I. Rybak and J. Magiera, “A multiple-time-step technique for coupled free flow and porous medium  systems,” J. Comput. Phys., vol. 272, pp. 327--342, 2014, doi: 10.1016/j.jcp.2014.04.036.
    27. W. L. Wendland, “Martin Costabel’s version of the trace theorem revisited,” Math. Methods Appl. Sci., vol. 37 (13), pp. 1924–1955, 2014.
  12. 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. 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.
    3. D. Fericean, T. Grosan, M. Kohr, and W. L. Wendland, “Interface boundary value problems of Robin-transmission type for  the Stokes and Brinkman systems on n-dimensional Lipschitz domains:  Applications,” Math. Methods Appl. Sci., vol. 36, pp. 1631–1648, 2013, doi: 10.1002/mma.2716.
    4. D. Fericean and W. L. Wendland, “Layer potential analysis for a Dirichlet-transmission problem in  Lipschitz domains in R^n,” ZAMM, vol. 93, pp. 762–776, 2013, doi: 10.1002/zamm.20100185.
    5. J. Giesselmann, “Cavitation and Singular Solutions in Nonlinear Elastodynamics,” in PAMM 13, in PAMM 13. Wiley, 2013, pp. 363–364. doi: 10.1002/pamm.201310177.
    6. J. Giesselmann, A. Miroshnikov, and A. E. Tzavaras, “The problem of dynamic cavitation in nonlinear elasticity,” in S�minaire Laurent Schwartz � EDP et applications, in S�minaire Laurent Schwartz � EDP et applications. 2013. [Online]. Available: http://slsedp.cedram.org/cedram-bin/article/SLSEDP_2012-2013____A14_0.pdf
    7. M. Kohr, C. Pintea, and W. L. Wendland, “Dirichlet-transmission problems for pseudodifferential Brinkman operators  on Sobolev and Besov spaces associated to Lipschitz domains in Riemannian  manifolds,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift  für Angewandte Mathematik und Mechanik, vol. 93, pp. 446–458, 2013, doi: 10.1002/zamm.201100194.
    8. M. Kohr, M. Lanza de Cristoforis, and W. L. Wendland, “Nonlinear Neumann-Transmission Problems for Stokes and Brinkman Equations  on Euclidean Lipschitz Domains,” Potential Analysis, vol. 38, pp. 1123–1171, 2013, doi: 10.1007/s.11118-012-9310-0.
    9. M. Kohr, C. Pintea, and W. L. Wendland, “Layer Potential Analysis for Pseudodifferential Matrix Operators  in Lipschitz Domains on Compact Riemannian Manifolds: Applications  to Pseudodifferential Brinkman Operators,” International Mathematics Research Notices, vol. 2013 (19), pp. 4499–4588, 2013, doi: 10.1093/imnr/run999.
    10. L. Ostrowski, “LQR control for Parametric Systems with Reduced Basis Controllers.” 2013.
    11. 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.
    12. 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.
    13. D. Seus, “Spektralasymptotiken auf dem Loopgraphen,” 2013.
  13. 2012

    1. G. L. Aki, J. Daube, W. Dreyer, J. Giesselmann, M. Kr�nkel, and C. Kraus, “A diffuse interface model for quasi-incompressible flows : Sharp  interface limits and numerics,” in ESAIM Proceedings Vol. 38, in ESAIM Proceedings Vol. 38. 2012, pp. 54–77. doi: 10.1051/proc/201238004.
    2. C. Appel, “Mathematische Methoden zur Bestimmung alterungskritischer Parameter  von Lithium-Ionen Zellen,” Diploma thesis, 2012.
    3. E. Audusse et al., “Sediment transport modelling : Relaxation schemes for Saint-Venant  - Exner and three layer models,” in ESAIM Proceedings Vol. 38, in ESAIM Proceedings Vol. 38. 2012, pp. 78–98. doi: 10.1051/proc/201238005.
    4. 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.
    5. F. Coquel, M. Gutnic, P. Helluy, F. Lagoutière, C. Rohde, and N. Seguin, Eds., CEMRACS 2011, Multiscale Coupling of Complex Models, vol. 38. ESAIM Proceedings, 2012.
    6. 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.
    7. 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
    8. 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.
    9. D. Garmatter, “Reduzierte Basis Methoden für lineare Evolutionsprobleme am Beispiel  von European Option Pricing,” Diploma thesis, 2012.
    10. J. Giesselmann, “Sharp interface limits for Korteweg Models,” in Hyperbolic Problems: Theory, Numerics, Applications, T. Li and S. Jiang, Eds., in Hyperbolic Problems: Theory, Numerics, Applications, vol. 2. 2012, pp. 422–430.
    11. J. Giesselmann and M. Wiebe, “Finite volume schemes for balance laws on time-dependent surfaces,” in Numerical Methods for Hyperbolic Equations, E. Vasquez-Cendon, A. Hidalgo, P. Garcia Navarro, and L. Cea, Eds., in Numerical Methods for Hyperbolic Equations. Taylor and Francis Group, 2012.
    12. H. Harbrecht, W. L. Wendland, and N. Zorii, “On Riesz minimal energy problems,” J. Math. Anal. Appl., vol. 393, no. 2, Art. no. 2, 2012, doi: 10.1016/j.jmaa.2012.04.019.
    13. A. S. Jackson, I. Rybak, R. Helmig, W. G. Gray, and C. T. Miller, “Thermodynamically constrained averaging theory approach for modeling  flow and transport phenomena in porous medium systems: 9. Transition  region models,” Adv. Water Res., vol. 42, pp. 71--90, 2012, doi: 10.1016/j.advwatres.2012.01.006.
    14. 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.
    15. 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.
    16. 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.
    17. M. Kohr, C. Pintea, and W. L. Wendland, “Potential analysis for pseudodifferential matrix operators in Lipschitz  domains on Riemannian manifolds: Applications to Brinkman operators.,” Mathematica, vol. 54, pp. 159–176, 2012.
    18. M. Kohr, G. P. Raja Sekhar, E. M. Ului, and W. L. Wendland, “Two-dimensional Stokes-Brinkman cell model---a boundary integral  formulation,” Appl. Anal., vol. 91, no. 2, Art. no. 2, 2012, doi: 10.1080/00036811.2011.614604.
    19. 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.
    20. U. Langer, M. Schanz, O. Steinbach, and W. L. Wendland, Eds., “Fast Boundary Element Methods on Engineering and Industrial Applications.” Springer, p. 269, 2012.
    21. 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.
    22. 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.
    23. C. Winkel, S. Neumann, C. Surulescu, and P. Scheurich, “A minimal mathematical model for the initial molecular interactions  of death receptor signalling,” Math. Biosci. Eng., vol. 9, pp. 663–683, 2012, doi: 10.3934/mbe.2012.9.663.
  14. 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, 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.
    2. J. Giesselmann, “Modelling and Analysis for Curvature Driven Partial Differential  Equations,” Universit�t Stuttgart, 2011.
    3. M. Kohr, C. Pintea, and W. L. Wendland, “Dirichlet-transmission problems for general Brinkman operators  on Lipschitz and $C^1$ domains in Riemannian manifolds,” Discrete Contin. Dyn. Syst. Ser. B, vol. 15, no. 4, Art. no. 4, 2011, doi: 10.3934/dcdsb.2011.15.999.
    4. T. A. Mel’nyk, Iu. A. Nakvasiuk, and W. L. Wendland, “Homogenization of the Signorini boundary-value problem in a thick  junction and boundary integral equations for the homogenized problem,” Math. Methods Appl. Sci., vol. 34, no. 7, Art. no. 7, 2011, doi: 10.1002/mma.1395.
    5. K. Mosthaf et al., “A coupling concept for two-phase compositional porous-medium and  single-phase compositional free flow,” Water Resour. Res., vol. 47, p. W10522, 2011, doi: 10.1029/2011WR010685.
    6. 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.
    7. W. L. Wendland, “Boundary element domain decomposition with Trefftz elements and Levi  fuctions,” in 19th Intern. Conf. on Computer Methods in Mechanics, in 19th Intern. Conf. on Computer Methods in Mechanics. Warsaw: Publ. House of Warsaw Univ. Technology, 2011.
    8. C. Winkel, S. Neumann, C. Surulescu, and P. Scheurich, “A minimal mathematical model for the initial molecular interactions  of death receptor signalling,” SRC SimTech, 2011. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=486
  15. 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, vol. 526, 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.
    3. L. Tobiska and C. Winkel, “The two-level local projection stabilization as an enriched one-level  approach. A one-dimensional study,” Int. J. Numer. Anal. Model., vol. 7, no. 3, Art. no. 3, 2010, [Online]. Available: http://www.math.ualberta.ca/ijnam/Volume-7-2010/No-3-10/2010-03-09.pdf
  16. 2009

    1. R. Ewing, O. Iliev, R. Lazarov, I. Rybak, and J. Willems, “A simplified method for upscaling composite materials with high contrast  of the conductivity,” SIAM J. Sci. Comp., vol. 31, no. 4, Art. no. 4, 2009, doi: 10.1137/080731906.
    2. J. Giesselmann, “A convergence result for finite volume schemes on Riemannian manifolds,” M2AN Math. Model. Numer. Anal., vol. 43, no. 5, Art. no. 5, 2009, [Online]. Available: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8194518
    3. 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.
    4. L. Tobiska and C. Winkel, “The two-level local projection stabilization as an enriched one-level  approach. A one-dimensional study,” Institute for Analysis and Computational Mathematics, Otto-von-Guericke  University Magdeburg, 2009. [Online]. Available: http://www.math.uni-magdeburg.de/up_preprints/preprint18_2009.pdf
  17. 2008

    1. 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.
    2. 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.
    3. J. Giesselmann, “Convergence Rate of Finite Volume Schemes for Hyperbolic Conservation  Laws on Riemannian Manifolds,” in Finite Volumes for Complex Applications 5, R. Eymard and J.-M. Herard, Eds., in Finite Volumes for Complex Applications 5. ISTE, Wiley, 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, [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
    5. G. C. Hsiao and W. L. Wendland, Boundary integral equations, vol. 164. in Applied Mathematical Sciences, vol. 164. Berlin: Springer-Verlag, 2008, p. xx+618. doi: 10.1007/978-3-540-68545-6.
    6. O. Iliev and I. Rybak, “On numerical upscaling for flows in heterogeneous porous media,” Comput. Methods Appl. Math., vol. 8, no. 1, Art. no. 1, 2008.
    7. 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.
    8. 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.
  18. 2007

    1. R. Ewing, O. Iliev, R. Lazarov, and I. Rybak, “On two-level preconditioners for flow in porous media,” Fraunhofer ITWM, 121, 2007.
    2. O. Iliev and I. Rybak, “On approximation property of multipoint flux approximation method,” Fraunhofer ITWM, 119, 2007.
    3. O. Iliev, I. Rybak, and J. Willems., “On upscaling heat conductivity for a class of industrial problems,” Fraunhofer ITWM, 120, 2007.
    4. 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.
    5. 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.
    6. H. Schmidt, M. Wiebe, B. Dittes, and M. Grundmann, “Meyer-Neldel rule in ZnO,” Applied Physics Letters, vol. 91, no. 23, Art. no. 23, 2007, doi: http://dx.doi.org/10.1063/1.2819603.
  19. 2006

    1. 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.
    2. 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.
    3. 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.
    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.
  20. 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, vol. 7, 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. 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.
    3. M. J. Gander and C. Rohde, “Nonlinear advection problems and overlapping Schwarz waveform relaxation,” in Domain decomposition methods in science and engineering, vol. 40, in Domain decomposition methods in science and engineering, vol. 40. , Berlin: Springer, 2005, pp. 251--258. doi: 10.1007/3-540-26825-1_23.
    4. 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.
    5. O. Iliev and I. Rybak, “On numerical upscaling of flow in anisotropic porous media,” in Mathematisches Forschungsinstitut Oberwolfach Report No. 20, in Mathematisches Forschungsinstitut Oberwolfach Report No. 20. 2005, pp. 1162–1165.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
  21. 2004

    1. 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.
    2. 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.
    3. P. Matus, R. Melnik, L. Wang, and I. Rybak, “Applications of fully conservative schemes in nonlinear thermoelasticity:  modelling shape memory materials,” Math. Comp. Simulation, vol. 65, pp. 489--509, 2004.
    4. P. Matus and I. Rybak, “Difference schemes for elliptic equations with mixed derivatives,” Comput. Methods Appl. Math., vol. 4, no. 4, Art. no. 4, 2004.
    5. M. Reisert, “Entwicklung von Algorithmen zur Lageinvarianten Merkmalsgewinnung  f�r Drahtgittermodelle,” Diploma Thesis, 2004.
    6. 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.
    7. I. Rybak, “Monotone and conservative difference schemes for elliptic equations  with mixed derivatives,” Math. Model. Anal., vol. 9, no. 2, Art. no. 2, 2004.
    8. I. Rybak, “Monotone and conservative difference schemes for equations with mixed  derivatives,” Dokl. Akad. Navuk Belarusi, vol. 48, no. 1, Art. no. 1, 2004.
    9. I. Rybak, “Computational dynamics of shape memory alloys,” in Proc. of Lobachevski Mathematical Center, in Proc. of Lobachevski Mathematical Center. Kazan, 2004, pp. 209--218.
    10. I. Rybak, “Monotone and conservative difference schemes for nonlinear nonstationary  equations and equations with mixed derivatives,” Institute of Mathematics of the National Academy of Sciences of Belarus, 2004.
    11. I. Rybak, “Monotone difference schemes for equations with mixed derivatives  in the case of boundary conditions of the third type,” Proceedings of the National Academy of Sciences of Belarus, Series  of Physical-Mathematical Sciences, vol. 40, no. 1, Art. no. 1, 2004.
  22. 2003

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. P. Matus, R. Melnik, and I. Rybak, “Fully conservative difference schemes for nonlinear models describing  dynamics of materials with shape memory,” Dokl. Akad. Navuk Belarusi, 47(1):15–17, 2003., vol. 47, no. 1, Art. no. 1, 2003.
    7. P. Matus and I. Rybak, “Monotone difference schemes for nonlinear parabolic equations,” Differential Equations, vol. 39, no. 7, Art. no. 7, 2003.
    8. R. Melnik, L. Wang, P. Matus, and I. Rybak, “Computational aspects of conservative difference schemes for shape  memory alloys applications,” Lecture Notes in Comput. Sci., vol. 2668, pp. 791--800, 2003.
    9. 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.
    10. I. Rybak, “Difference schemes for nonlinear models describing dynamic behaviour  of shape memory alloys,” in Condensed State Physics: XI Republican Scientific Conference, Grodno,  Belarus, April 23�25, 2003, in Condensed State Physics: XI Republican Scientific Conference, Grodno,  Belarus, April 23�25, 2003. 2003, pp. 200–203.
  23. 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. 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.
    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. 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.
  24. 2001

    1. 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.
    2. 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, in Hyperbolic problems: theory, numerics, applications, Vol. I,  II (Magdeburg, 2000), vol. 141. , Basel: Birkhäuser, 2001, pp. 277--286.
    3. 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.
    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, in Hyperbolic problems: theory, numerics, applications, Vol. I,  II (Magdeburg, 2000), vol. 141. , Basel: Birkhäuser, 2001, pp. 399--408.
    5. 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.
    6. 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.
    7. 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.
    8. R. Klöfkorn, “Simulation von Abbau- und Transportprozessen gelöster Schadstoffe  im Grundwasser,” Diploma thesis, Albert-Ludwigs-Universität Freiburg, 2001.
    9. 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.
  25. 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.
  26. 1999

    1. 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.
    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, in Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich,  1998), vol. 129. , Basel: Birkhäuser, 1999, pp. 333--342.
  27. 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.
    3. K. G. Siebert, “Einführung in die numerische Behandlung der Navier-Stokes-Gleichungen.” 1998.
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