Publications

List of publications of the Chair of Applied Mathematics.

  1. 2025

    1. Anamika, R. Barthwal, and T. R. Sekhar, “Construction of solutions to a Riemann problem for a two-dimensional Keyfitz-Kranzer type model governing thin film flow,” Accepted for publication at Applied Mathematics and Computation, 2025.
    2. R. Barthwal and C. Rohde, “A hyperbolic model for two-layer thin film flow with a perfectly soluble anti-surfactant.” 2025. [Online]. Available: https://arxiv.org/abs/2502.17205
    3. L. Duvenbeck, C. Riethmüller, and C. Rohde, “Data-driven geometric parameter optimization for PD-GMRES.” 2025. doi: https://doi.org/10.48550/arXiv.2503.09728.
    4. T. Ghosh, C. Bringedal, C. Rohde, and R. Helmig, “A phase-field approach to model evaporation from porous media: Modeling and upscaling,” Advances in Water Resources, p. 104922, 2025, doi: https://doi.org/10.1016/j.advwatres.2025.104922.
    5. Q. Huang, C. Rohde, W.-A. Yong, and R. Zhang, “A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility,” J. Differential Equations, vol. 438, p. 113339, 2025, doi: 10.1016/j.jde.2025.113339.
    6. C. Rohde and F. Wendt, “Mathematical Justification of a Baer-Nunziato Model for a Compressible Viscous Fluid with Phase Transition.” 2025. [Online]. Available: https://arxiv.org/abs/2504.10161
    7. L. Ruan and I. Rybak, “A hybrid-dimensional Stokes-Brinkman-Darcy model for arbitrary flows to the fluid-porous interface,” Transp. Porous Med. (submitted), 2025.
    8. T. Schollenberger, C. Rohde, and R. Helmig, “Two-phase pore-network model for evaporation-driven salt precipitation -- representation and analysis of pore-scale processes.” 2025. [Online]. Available: https://arxiv.org/abs/2503.22533
    9. A. Schwarz, J. Keim, C. Rohde, and A. Beck, “Entropy stable shock capturing for high-order DGSEM on moving meshes.” 2025. [Online]. Available: https://arxiv.org/abs/2503.23237
    10. A. Schwarz, D. Kempf, J. Keim, P. Kopper, C. Rohde, and A. Beck, “Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows.” 2025. [Online]. Available: https://arxiv.org/abs/2504.00173

  2. 2024

    1. A. F. Albişoru, M. Kohr, I. Papuc, and W. L. Wendland, “On some Robin–transmission problems for the Brinkman system and a Navier–Stokes type system,” Math. Meth. Appl. Sci., pp. 1–28, 2024, doi: https://doi.org/10.1002/mma.10170.
    2. M. Alkämper, J. Magiera, and C. Rohde, “An Interface-Preserving Moving Mesh in Multiple Space Dimensions,” ACM Trans. Math. Softw., vol. 50, Art. no. 1, Mar. 2024, doi: 10.1145/3630000.
    3. R. Barthwal and T. R. Sekhar, “On a degenerate boundary value problem to relativistic magnetohydrodynamics with a general pressure law,” Zeitschrift für angewandte Mathematik und Physik, Art. no. 75, 2024, doi: 10.1007/s00033-024-02354-0.
    4. G. C. Hsiao, T. Sánchez-Vizuet, and W. L. Wendland, “Boundary-field formulation for transient electromagnetic scattering by dielectric scatterers and coated conductors,” SIAM J. Math. Analysis, to appear, 2024. doi: https://doi.org/10.48550/arXiv.2406.05367.
    5. 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, Art. no. 1, 2024, doi: 10.3934/nhm.2024006.
    6. J. Keim, H.-C. Konan, and C. Rohde, “A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow.” 2024. [Online]. Available: https://arxiv.org/abs/2412.11904
    7. M. Kohr, V. Nistor, and W. L. Wendland, “The Stokes operator on manifolds with cylindrical ends,” Journal of Differential Equations, Art. no. 407, 2024, doi: https://doi.org/10.1016/j.jde.2024.06.017.
    8. M. Lukácová-Medvid’ová and C. Rohde, “Mathematical Challenges for the Theory of Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness,” Jahresber. Dtsch. Math.-Ver., vol. 126, Art. no. 4, 2024, doi: 10.1365/s13291-024-00290-6.
    9. J. Magiera and C. Rohde, “A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate,” Communications on Applied Mathematics and Computation, 2024, doi: 10.1007/s42967-023-00349-8.
    10. T. A. Mel’nyk and T. Durante, “Spectral problems with perturbed Steklov conditions in thick junctions with branched structure.,” Applicable Analysis, pp. 1–26, 2024, doi: https://doi.org/10.1080/00036811.2024.2322644.
    11. T. Mel’nyk and C. Rohde, “Asymptotic expansion for convection-dominated transport in a thin graph-like junction.,” Analysis and Applications, vol. 22 (05), pp. 833–879, 2024, doi: https://doi.org/10.1142/S0219530524500040.
    12. 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, Art. no. 1, 2024, doi: 10.1016/j.jmaa.2023.127587.
    13. T. Mel’nyk and C. Rohde, “Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains,” Nonlinear Differ. Equ. Appl., vol. 31:105, 2024, doi: https://doi.org/10.1007/s00030-024-00997-6.
    14. 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. 137, pp. 27–52, 2024, doi: 10.3233/ASY-231876.
    15. T. Mel’nyk and C. Rohde, “Muskat-Leverett two-phase flow in thin cylindric porous media: Asymptotic approach.” 2024. [Online]. Available: https://arxiv.org/abs/2411.02923
    16. Y. Miao, C. Rohde, and H. Tang, “Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities,” Stoch. Partial Differ. Equ. Anal. Comput., vol. 12, Art. no. 1, 2024, doi: 10.1007/s40072-023-00291-z.
    17. L. Ruan and I. Rybak, “Stokes-Brinkman-Darcy models for coupled fluid-porous systems: derivation, analysis and validation,” Appl. Math. Comp. (submitted), 2024.
    18. T. Schollenberger, L. von Wolff, C. Bringedal, I. S. Pop, C. Rohde, and R. Helmig, “Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models,” Transport in Porous Media, Oct. 2024, doi: 10.1007/s11242-024-02125-5.
    19. P. Strohbeck, M. Discacciati, and I. Rybak, “Optimized Schwarz method for the Stokes-Darcy problem with generalized interface conditions,” J. Comput. Phys. (submitted), 2024.
    20. W. L. Wendland, “On the construction of the Stokes flow in a domain with cylindrical ends,” Math. Meth. Appl. Sci., pp. 1–6, 2024, doi: https://doi.org/10.1002/mma.10106.

  3. 2023

    1. 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.
    2. S. Burbulla, M. Hörl, and C. Rohde, “Flow in Porous Media with Fractures of Varying Aperture,” SIAM J. Sci. Comput, vol. 45, Art. no. 4, 2023, doi: 10.1137/22M1510406.
    3. 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., Springer Nature Switzerland, 2023, pp. 275–283. doi: 10.1007/978-3-031-40864-9_22.
    4. 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, Art. no. 1, 2023, doi: 10.1137/21M1415005.
    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., Cham: Springer International Publishing, 2023, pp. 443–450.
    6. 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.
    7. M. Kohr, V. Nistor, and W. L. Wendland, “Layer potentials and essentially translation invariant pseudodifferential operators on manifolds with cylindrical ends,” Postpandemic Operator Theory, Springer-Verlag Berlin, pp. 61–115, 2023. [Online]. Available: https://doi.org/10.48550/arXiv.2308.06308
    8. 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.
    9. T. A. Mel’nyk, Complex Analysis. Springer Nature Switzerland, 2023. doi: https://doi.org/10.1007/978-3-031-39615-1.
    10. T. A. Mel’nyk, “Asymptotic analysis of spectral problems in thick junctions with the branched fractal structure,” Mathematical Methods in the Applied Sciences, vol. 46, Art. no. 3, 2023, doi: https://doi.org/10.1002/mma.8692.
    11. 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.
    12. 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.
    13. 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., Springer Nature Switzerland, 2023, pp. 365–373. doi: 10.1007/978-3-031-40864-9_31.
    14. D. Seus, F. A. Radu, and C. Rohde, “Towards hybrid two-phase modelling using linear domain decomposition,” Numer. Methods Partial Differential Equations, vol. 39, Art. no. 1, 2023, doi: https://doi.org/10.1002/num.22906.
    15. 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, Art. no. 3, Apr. 2023, doi: 10.1007/s11242-023-01919-3.
    16. 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., Springer Nature Switzerland, 2023, pp. 375–383. doi: 10.1007/978-3-031-40864-9_32.
    17. W. L. Wendland, “My relation with GAMM,” GAMM Rundbrief. [Online]. Available: https://www.gamm.org/wp-content/uploads/2024/03/GAMM_1-23_web.pdf

  4. 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, 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, “Interface conditions for arbitrary flows in Stokes-Darcy systems : derivation, analysis and validation.” Universität Stuttgart, 2022. doi: 10.18419/OPUS-12573.
    4. 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.
    5. 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, Art. no. 1, 126464, 2022, [Online]. Available: https://doi.org/10.1016/j.jmaa.2022.126464
    6. 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.
    7. T. Mel’nyk and A. V. Klevtsovskiy, “Asymptotic expansion for the solution of a convection-diffusion problem in a thin graph-like junction,” Asymptotic Analysis, vol. 130, Art. no. 3–4, 2022, doi: 10.3233/ASY-221761.

  5. 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, p. Paper No. 98, 55, 2021.
    2. 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), Art. no. 0, 2021, doi: 10.1080/00036811.2021.1986027.
    3. T. Mel’nyk, “Asymptotic approximations for eigenvalues and eigenfunctions of a spectral problem in a thin graph-like junction with a concentrated mass in the node,” Analysis and Applications, vol. 19, Art. no. 05, 2021, doi: 10.1142/S0219530520500219.
    4. 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, Art. no. 1, 2021, doi: 10.1007/s00030-020-00661-9.

  6. 2020

    1. 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.

  7. 2019

    1. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” Computational Geosciences, vol. 23, Art. no. 2, Apr. 2019, doi: 10.1007/s10596-018-9785-x.

  8. 2014

    1. 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., AIMS, 2014, pp. 599–606. [Online]. Available: https://aimsciences.org/books/am/AMVol8.html

  9. 2013

    1. M. A. Dihlmann and B. Haasdonk, “Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems,” University of Stuttgart (The final publication is available at Springer via http://dx.doi.org/10.1007/s10589-014-9697-1), SimTech Preprint, 2013.

  10. 2012

    1. D. Garmatter, “Reduzierte Basis Methoden für lineare Evolutionsprobleme am Beispiel von European Option Pricing,” Diploma thesis, 2012.

  11. 2011

    1. B. Kabil, “On the asymptotics of solutions to resonator equations,” Hyperbolic Problems: Theory, Numerics, Applications, vol. 8, pp. 373–380, 2011, [Online]. Available: https://aimsciences.org/books/am/AMVol8.html

  12. 2009

    1. B. Haasdonk and M. Ohlberger, “Space-Adaptive Reduced Basis Simulation for Time-Dependent Problems,” in Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling, 2009. [Online]. Available: http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_Nadapt.pdf
    2. B. Haasdonk and M. Ohlberger, “Efficient Reduced Models for Parametrized Dynamical Systems by Offline/Online Decomposition,” in Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling, 2009. [Online]. Available: http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_PMOR.pdf

  13. 2001

    1. 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, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.
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