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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, arXiv preprint arXiv:2402.15361
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
Rémi Abgrall, Wasilij Barsukow, Christian Klingenberg: The Active Flux method for the Euler equations on Cartesian grids, arXiv:2310.00683, submitted 2023
Niklas Kolbe, Michael Herty, Siegfried Müller. Numerical schemes for coupled systems of nonconservative hyperbolic equations, arXiv preprint arXiv:2311.03581, submitted 2023.
Michael Herty, Niklas Kolbe, Siegfried Mueller: A central scheme for two coupled hyperbolic systems, Preprint: A central scheme for coupled hyperbolic systems, arXiv:2304.13946, submitted 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,