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Wasilij Barsukow, Praveen Chandrashekar; Christian Klingenberg; Lisa Lechner: "A generalized Active Flux method of arbitrarily high order in two dimensions”, https://arxiv.org/abs/2502.05101, (2025)
Wasilij Barsukow, Janina Kern, Christian Klingenberg, Lisa Lechner: "Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform", https://arxiv.org/abs/2412.03477, (2025)
Junming Duan, Wasilij Barsukow, Christian Klingenberg: Active flux methods for hyperbolic conservation laws - flux vector splitting and bound-preservation, SIAM Journal on Scientific Computing, https://arxiv.org/abs/2411.00065, (2025)
Rémi Abgrall, Wasilij Barsukow, Christian Klingenberg: The Active Flux method for the Euler equations on Cartesian grids, Journal of Scientific Computing, Volume 102, article no.36, https://arxiv.org/abs/2310.00683, (2025)
Anika Beckers, Niklas Kolbe: The Lax-Friedrichs method in one-dimensional hemodynamics, arXiv preprint
arXiv:2501.16115, (2025)
Giada Cianfarani Carnevale, Jan Giesselmann: Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness, arXiv preprint arXiv:2501.02915, (2025)
Niklas Kolbe, Michael Herty, Siegfried Müller. Numerical schemes for coupled systems of nonconservative hyperbolic equations, SIAM J. Numer. Anal., 62(5):2143-2171, DOI:10.1137/23M1615176
Michael Herty, Kai Hinzmann, Siegfried Müller, Ferdinand Thein: Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations, arXiv preprint arXiv:2410.21890, October 2024
Kharisma Surya Putri, Tatsuki Mizuochi, Niklas Kolbe, Hirofumi Notsu: Error estimates for first- and second-order Lagrange–Galerkin moving mesh schemes for the one-dimensional convection–diffusion equation, J. Sci. Comput., 101(2):37, DOI:10.1007/s10915-024-02673-4
Niklas Kolbe, Siegfried Müller: A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid, arXiv preprint arXiv:2409.05473, September 2024
Michael Herty, Niklas Kolbe, Michael Neidlin: A one-dimensional model for aspiration therapy in blood vessels, arXiv preprint arXiv:2403.05494, March 2024
Michael Herty, Niklas Kolbe, Siegfried Mueller: A central scheme for two coupled hyperbolic systems, Commun. Appl. Math. Comput. 6, 2093–2118, DOI:10.1007/s42967-023-00306-5
Gunnar Birke, Christian Engwer, Jan Giesselmann, Sandra May: Error analysis of a first-order DoD cut cell method for 2D unsteady advection, arXiv preprint https://arxiv.org/abs/2411.10283,(2024)
Mária Lukácová-Medvid’ová, Christian Rohde: Mathematical Challenges for the Theory of Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness, Jahresbericht der Deutschen Mathematiker-Vereinigung 2024, https://doi.org/10.1365/s13291-024-00290-6
Mária Lukáčová-Medvid’ová, Yuhuan Yuan: Convergence of a generalized Riemann problem scheme for the Burgers equation, Commun. Appl. Math. Comput. 6, 2215–2238 (2024). https://doi.org/10.1007/s42967-023-00338-x
Erik Chudzik, Christiane Helzel, Mária Lukáčová-Medvid’ová: Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics. J Sci Comput 99, 16 (2024). https://doi.org/10.1007/s10915-024-02462-z
Alina Chertock, Michael Herty, Arsen S. Iskhakov, Safa Janajra, Alexander Kurganov, Mária Lukáčová-Medvid’ová: New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties, Commun. Appl. Math. Comput. 6 (2024), no. 3, 2011–2044. https://doi.org/10.1007/s42967-024-00392-z
Eduard Feireisl, Mária Lukáčová-Medvid’ová, Bangwei She et al.: Convergence of Numerical Methods for the Navier–Stokes–Fourier System Driven by Uncertain Initial/Boundary Data. Found Comput Math (2024). https://doi.org/10.1007/s10208-024-09666-7
Alina Chertock, Michael Herty, Alexander Kurganov, Mária Lukáčová-Medvid’ová: Challenges in stochastic Galerkin methods for nonlinear systems with uncertainty, Springer Volume on Advances in Nonlinear Hyperbolic Partial Differential Equations, (2024), accepted.
Mária Lukáčová-Medvid’ová, Bangwei She, Yuhuan Yuan: What is a Limit of Structure-preserving
Numerical Methods for Compressible Flows?, Numerical Mathematics and Advanced Applications, ENUMATH 2023 Proceedings Volume, (2024), accepted.
Matthias Kunik, Adrian Kolb, Siegfried Müller, Ferdinand Thein: Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions, J Comp Physics (2024), https://doi.org/10.1016/j.jcp.2024.113330
Junming Duan, Wasilij Barsukow, Christian Klingenberg: Active flux methods for hyperbolic conservation laws – flux vector splitting and bound-preservation: two-dimensional case, arXiv.2407.13380, submitted
Junming Duan, Wasilij Barsukow, Christian Klingenberg: Active flux methods for hyperbolic conservation laws – flux vector splitting and bound-preservation: one-dimensional case, arXiv:2405.02447, submitted
Sina Dahm, Jan Giesselmann, Christiane Helzel: Numerical discretisation of hyperbolic systems of moment equations describing sedimentation in suspensions of rod-like particles, Journal of Computational Physics, Vol. 513, p. 113162, 2024, https://doi.org/10.1016/j.jcp.2024.113162
Jan Friedrich, Simone Göttlich, Alexander Keimer, Lukas Pflug: Conservation laws with nonlocal velocity - the singular limit problem, SIAM J. Appl. Math., 84(2):497-522, 2024. https://doi.org/10.1137/22M1530471
Aaron Brunk, Jan Giesselmann, Maria Lukacova-Medvidova: Robust a posteriori error control for the Allen-Cahn equation with variable mobility, arXiv:2403.08898
Fabio Leotta, Jan Giesselmann: A priori error estimates of Runge-Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws, ESAIM: M2AN, 58 (4), 1301–1315, 2024. https://doi.org/10.1051/m2an/2024043
Matthias Kunik, Adrian Kolb, Siegfried Müller, Ferdinand Thein: Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions, arXiv preprint arXiv:2402.12857, February 2024
Michele Coti Zelati, Theodore D. Drivas, Rishabh S. Gvalani: Statistically self-similar mixing by Gaussian random fields, arXiv preprint arXiv:2309.15744, submitted September 2023
Felisia Chiarello, Jan Friedrich, Simone Göttlich: A non-local traffic flow model for 1-to-1 junctions with buffer arXiv:2307.09786, 2023
Michael Herty, Niklas Kolbe, Siegfried Mueller, Central schemes for networked scalar conservation laws, Networks and Heterogeneous Media, 18(1), 310--340, 2023, DOI:10.3934/nhm.2023012
Dmitri Kuzmin, Mária Lukácova-Medvid'ová, Philipp Öffner: Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems, arXiv:2308.14872, submitted 2023,