2026
E. Feireisl, , M. Lukacova-Medvidova, H. Mizerova, C. Yu; "Monte Carlo method and the random isentropic Euler system", Stoch. Partial Differ. Equ. Anal. Comput, https://doi.org/10.1007/s40072-026-00417-z (2026)
Yangyang Cao, Qian Huang, Julian Koellermeier, Alexander Kurganov, Yongle Liu: "Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations", Computers & Fluids, vol. 311, p. 107036, https://doi.org/10.1016/j.compfluid.2026.107036 (2026)
Jan Giesselmann, Hendrik Ranocha: "Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions", SMAI J. Comput. Math (2026)
Keim, J., Schwarz, A., Kopper, P., Blind, M., Rohde, C., Beck, A.: Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes. J. Comput. Phys. 114829 (2026). https://doi.org/10.1016/j.jcp.2026.114829
Barthwal, R., Rohde, C., Sen, A.: Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model. Nonlinearity. 39, Paper No. 035006 (2026). https://doi.org/10.1088/1361-6544/ae4afc
Barthwal, R., Rohde, C., Wang, Y.: A Generalized Riemann Problem Solver for a Hyperbolic Model of Two-Layer Thin Film Flow. J. Sci. Comput. 106, Paper No. 25 (2026). https://doi.org/10.1007/s10915-025-03151-1
Georgy Zinchenko, Jörg Schumacher: "Extending the Duchon-Robert framework for anomalous dissipation to compressible fluid flows", doi.org/10.1103/gspz-gv9w (2026)
Wasilij Barsukow, Praveen Chandrashekar; Christian Klingenberg; Lisa Lechner: "A generalized Active Flux method of arbitrarily high order in two dimensions", Computers & Fluids (2026) https://tinyurl.com/24yahz89
Gunnar Birke, Christian Engwer, Jan Giesselmann, Sandra May: Error analysis of a first-order DoD cut cell method for 2D unsteady advection, J Sci Comput 106, 1 (2026). https://doi.org/10.1007/s10915-025-03091-w
Jan Giesselmann, Philipp ̈Offner, Robert Sauerborn: "Convergence of a Finite Volume Scheme for the Navier-Stokes-Korteweg Model via Dissipative Solutions", arxiv:2604.16110 (2026)
A. Gjesteland, S. Ortleb, S. Elghawi, and D. C. D. R. Fernández, “Stable and asymptotic preserving space-time discretisations of a linear kinetic transport equation in diffusive scaling,” arXiv.2604.21752 (2026)
Jan Glaubitz, Armin Iske, Joshua Lampert, Philipp Öffner: "Why summation by parts is not enough" arxiv:2602.10786 (2026)
Thomas Eiter, Jan Giesselmann, Robert Lasarzik, Philipp Öffner, Robert Sauerborn: "Convergence analysis for a finite-volume scheme for the Euler- and Navier-Stokes-Korteweg system via energy-variational solutions" arxiv:2603.29880 (2026)
Philipp Öffner, Per Pettersson, Andrew R. Winters: "A high-order, structure preserving scheme for the stochastic Galerkin shallow water equations -- unification and two-dimensional extension" arxiv:2604.01199 (2026)
Jan Giesselmann, Philipp Öffner, Robert Sauerborn: "Convergence of a Finite Volume Scheme for the Navier-Stokes-Korteweg Model via Dissipative Solutions", arxiv:2604.16110 (2026)
Rahul Barthwal, Philipp Öffner, Christian Rohde Global Existence for a Class of Keyfitz--Kranzer Systems with Application to Thin-Film Flows. 2026, arXiv:2604.16000
Qian Huang, Simon Görtz, Paul Hollmann, Johannes Conrad, Christian Rohde, Martin Oberlack: A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation. 2026 arXiv:2604.15551
E. Feireisl, M. Lukacova-Medvidova, B. She, Y. Yuan: Temperature-driven turbulence in compressible fluid flows, arxiv:2603.28158
Marco Artiano, Hendrik Ranocha, Saurav Samantaray: "Asymptotic-Preserving and Well-Balanced Linearly Implicit IMEX Schemes for the Anelastic Limit of the Isentropic Euler Equations with Gravity", arxiv:2604.11573 (2026)
M. Anandan, K.R. Arun, A. Krishnamurty, M. Lukacova-Medvidova: "Error analysis of an asymptotic-preserving, energy-stable finite volume method for barotropic Euler equations", arxiv.org:2603.27421 (2026)
E. Feireisl, M. Lukacova-Medvidova, B. She, Y. Yuan: "Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system", arxiv.org:2603.20758 (2026)
M. Lukacova-Medvidova, B. She: "Lax convergence theorems and error estimates of a finite element method for the incompressible Euler system", arxiv.org:2604.00783 (2026)
A. Brunk, A. Jüngel, M. Lukacova-Medvidova: A structure-preserving numerical method for quasi-incompressible Navier--Stokes--Maxwell--Stefan systems, arXiV:2504.11892, accepted to J. Sci. Comput. 2026
A. Chertock, M. Herty, A. Ishakov, A. Ishakova, A. Kurganov, M. Lukacova-Medvidova: "Numerical study of random Kelvin-Helmholtz instability", arXiv:2511.00008 accepted to Comm. Comp. Phys. (2026)
E. Feireisl, , A. Jüngel, M. Lukacova-Medvidova: "Maximal dissipation and well-posedness of the Euler system of gas dynamic", accepted to ARMA, arXiv:2501.05134 (2026)
2025
Giada Cianfarani Carnevale, Jan Giesselmann: Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness, Comm. Math. Sci., Volume 23, no. 7, 1983-1998, https://dx.doi.org/10.4310/CMS.250802033320 (2025)
Aaron Brunk, Jan Giesselmann, Maria Lukacova-Medvidova: Robust a posteriori error control for the Allen-Cahn equation with variable mobility, SIAM J. Num. Anal., Volume 63, no. 4, 1540-1560, https://doi.org/10.1137/24M1646406 (2025)
Deniz A. Bezgin, Aaron B. Buhendwa, Steffen J. Schmidt, Nikolaus A. Adams: "ML-ILES: End-to-end optimization of data-driven high-order Godunov-type finite-volume schemes for compressible homogeneous isotropic turbulence", Journal of Computational Physics, Volume 522, 113560, https://doi.org/10.1016/j.jcp.2024.113560 (2025)
Hendrik Ranocha, Mario Ricchiuto: "Structure-Preserving Approximations of the Serre-Green-Naghdi Equations in Standard and Hyperbolic Form", Numerical Methods for Partial Differential Equations, Volume 41, Issue 4, e70016, https://doi.org/10.1002/num.70016 (2025)
Luis Kaiser, Richard Tsai, Christian Klingenberg: “Efficient Numerical Wave Propagation Enhanced by an End-to-End Deep Learning Model", Proceedings of 'Numerical Mathematics and Advanced Applications (ENUMATH 2023)', Springer Lecture Notes in Computational Science and Engineering, vol. 154, pp. 12 - 22, https://tinyurl.com/4nay64e8 (2025)
Qiang Huang, Christian Rohde, Wen-An Yong, Ruixi Zhang : "A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility", J. Differential Equations. 438, 113339 (2025). https://doi.org/10.1016/j.jde.2025.113339
M. Ciallella, L. Micalizzi, V. Michel-Dansac, P. Öffner, and D. Torlo - A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations, GEM - International Journal on Geomathematics, https://link.springer.com/article/10.1007/s13137-025-00262-7 ,2025
P. Öffner, L. Petri, and D. Torlo - Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations - Applied Numerical Mathematics, https://www.sciencedirect.com/science/article/pii/S0168927424003568?via%3Dihub, 2025
H. Ranocha, A. R. Winters, M. Schlottke-Lakemper, P. Öffner, J. Glaubitz, G. J. Gassner - High-order upwind summation-by-parts methods for nonlinear conservation laws - Journal of Computational Physics 520, https://www.sciencedirect.com/science/article/pii/S0021999124007198?via%3Dihub, (2025)
Timo Böhme, Simone Göttlich, Andreas Neuenkirch: "A nonlocal traffic flow model with stochastic velocity", ESAIM: M2AN, 59 1 (2025) 487-518, https://doi.org/10.1051/m2an/2024082, (2025)
Niklas Kolbe, Siegfried Müller, A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid, Applied Mathematics and Computation 504, (2025). https://doi.org/10.1016/j.amc.2025.129503
Michael Herty, Kai Hinzmann, Siegfried Müller, Ferdinand Thein, Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations, Mathematical Control and Related Fields (2025) https://doi.org/10.3934/mcrf.2025056
D. Breit, T. C. Moyo, and P. Öffner - Discontinuous Galerkin methods for the complete stochastic Euler equations, Journal of Computational Physics 541 (2025). https://doi.org/10.1016/j.jcp.2025.114324
H. Hajduk, D. Kuzmin, P. Öffner, G. Lube - Locally Energy-Stable Finite Element Schemes for Incompressible Flow Problems: Design and Analysis for Equal-Order Interpolations, Computers & Fluids 294 (2025). https://doi.org/10.1016/j.compfluid.2025.106622
Glaubitz, J., Nordström, J. & Öffner, P. An Optimization-Based Construction Procedure for Function Space-Based Summation-by-Parts Operators on Arbitrary Grids. J Sci Comput 105, 83 (2025). https://doi.org/10.1007/s10915-025-03062-1
D. Kuzmin, S. Lee, Y.-Y. Yang.: Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equations, Journal of Computational Physics 541 (2025). https://doi.org/10.1016/j.jcp.2025.114323
I. Timofeyev, A. Schwarzmann, D. Kuzmin, Application of machine learning and convex limiting to subgrid flux modeling in the shallow-water equations, Mathematics and Computers in Simulation 238 (2025). https://doi.org/10.1016/j.matcom.2025.04.031
Abgrall, R., Barsukow, W. & Klingenberg, C. A Semi-discrete Active Flux Method for the Euler Equations on Cartesian Grids. J Sci Comput 102, 36 (2025). https://doi.org/10.1007/s10915-024-02749-1
M. Anandan, M. Lukacova-Medvidova: Provably fully discrete energy-stable and asymptotic-preserving scheme for barotropic Euler equations, arXiv:2511.19679 (2025)
S. Cu, A. Kurganov, M. Lukacova-Medvidova, M. Na: A Locally Divergence-Free Local Characteristic Decomposition Based Path-Conservative Central-Upwind Scheme for Ideal Magnetohydrodynamics, arXiv:2512.16346 (2025)
Christian Rohde, Florian Wendt: Mathematical Justification of a Baer-Nunziato Model for a Compressible Viscous Fluid with Phase Transition, 2025, arXiv:2504.10161
Nilias Chaudhuri, Christian Rohde, Florian Wendt: Weak-Strong Uniqueness and Relaxation Limit for a Navier-Stokes-Korteweg Model, 2025, arXiv:2512.09719
Christian Rohde, Florian Wendt: Effective Equations for a Compressible Liquid-Vapor Flow Model with Highly Oscillating Initial Density, 2025, arXiv:2512.15535
Rahul Barthwal, Firas Dhaouadi, Christian Rohde.: On hyperbolic approximations for a class of dispersive and diffusive-dispersive equations, 2025, arXiv:2512.04882
Gianluca Crippa: "Introduction to the theory of mixing for incompressible flows" arXiv:2511.03360 (2025)
C Fan, Q Huang, K Wu.: "Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations", arXiv:2510.18380 (2025)
Thomas Eiter, Stefanie Schindler: "Time-asymptotic self-similarity of the damped compressible Euler equations in parabolic scaling variables", arXiv:2507.03688 (2025)
Ferdinand Thein, Hendrik Ranocha: "Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods", arXiv:2508.21427 (2025)
Louis Petri, Gunnar Birke, Christian Engwer, Hendrik Ranocha: "The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable", arXiv:2508.05372 (2025)
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner, Jan Nordström, Sigrun Ortleb, Hendrik Ranocha: "Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators", arXiv:2507.11068 (2025)
Junming Duan, Wasilij Barsukow, Christian Klingenberg: "An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling", arXiv:2508.05166 (2025)
Christian Klingenberg, Simon Markfelder, Emil Wiedemann: "Maximal turbulence as a selection criterion for measure-valued solutions", submitted, https://arxiv.org/abs/2503.20343 (2025)
Robert Lasarzik: "Energy-variational structure in evolution equations", https://arxiv.org/abs/2503.11438, (2025)
Arne Berrens, Jan Giesselmann: "A posteriori error control for a finite volume scheme for a cross-diffusion model of ion transport", https://arxiv.org/abs/2502.08306 (2025)
Sanjibanee Sudha, Jan Friedrich, Samala Rathan: "Convergence of the non-staggered Nessyahu-Tadmor scheme for coupled systems of one-dimensional nonlocal balance laws" arxiv.org:2501.14425 (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)
M. Lukacova-Medvidova, Z. Tang, Y. Yuan: "Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems", arxiv:2511.00957, accepted to Comm. Comp. Phys. (2025)
M. Lukacova-Medvidova, S. Schneider: "Random compressible Euler flows", Proceeding HYP 2024, preprint, (2025)
Maria Colombo, Gianluca Crippa, Laura V. Spinolo: "On multidimensional nonlocal conservation laws with BV kernels" Indiana University Mathematics Journal, arxiv:2408.02423 (2025)
2024
V. Stegmayer, S. Görtz, S. Akbari, and M. Oberlack. “On the Lundgren hierarchy of helically symmetric turbulence”. In: Fluid Dynamics Research (2024), p. 041402
S. Ortleb: "On Unconditional Stability of Upwind Generalized Summation-by-Parts Schemes for Kinetic Equations in the Diffusion Limit", PAMM (2024)
S. G. Krupa and L. Székelyhidi, Jr. Nonexistence of T4 configurations for hyperbolic systems and the Liu entropy condition. Adv. Math., 454: Paper No. 109856, (2024)
D. W. Boutros, S. Markfelder, E. S. Titi: Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations. J. Nonlinear Sci. 34(4), Article Number 68 (2024)
S. Markfelder: A New Convex Integration Approach for the Compressible Euler Equations and Failure of the Local Maximal Dissipation Criterion. Nonlinearity 37(11), 1-60 (2024)
Georgy Zinchenko , Vladyslav Pushenko , and Jörg Schumacher: "Local precursors to anomalous dissipation in Navier-Stokes turbulence: Burgers vortex-type models and simulation analysis", Phys. Rev. Fluids 9, 114608 (2024)
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito: "Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations" Mathematics in Engineering, Volume 6, Issue 4: 494-509. doi: 10.3934/mine.2024020
Herty, Michael and Thein, Ferdinand: Boundary feedback control for hyperbolic systems, https://doi.org/10.1051/cocv/2024062, (2024)
J. Glaubitz, S.-Ch. Klein, J. Nordström, P. Öffner - Summation-by-parts operators for general function spaces: The second derivative - Journal of Computational Physics 504, 2024. https://www.sciencedirect.com/science/article/pii/S0021999124001384
Agosti, Abramo, Lasarzik, Robert and Rocca, Elisabetta: "Energy-variational solutions for viscoelastic fluid models" Advances in Nonlinear Analysis, vol. 13, no. 1, 2024, pp. 20240056. https://doi.org/10.1515/anona-2024-0056
Felisia Chiarello, Jan Friedrich, Simone Göttlich: "A non-local traffic flow model for 1-to-1 junctions with buffer", Netw. Heterog. Media, 19(1):405-429, 2024, https://www.aimspress.com/article/doi/10.3934/nhm.2024018
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
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
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
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
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
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
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
Michele Coti Zelati, Theodore D. Drivas, Rishabh S. Gvalani: Mixing by Statistically Self-similar Gaussian Random Fields, J Stat Phys 191, 61 (2024). https://doi.org/10.1007/s10955-024-03277-w
Michael Herty, Niklas Kolbe, Michael Neidlin: A one-dimensional model for aspiration therapy in blood vessels, arXiv preprint arXiv:2403.05494, March 2024
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
Abhishek Chaudhary, Ujjwal Koley, Emil Wiedemann: "Dissipative measure-valued solutions and weak-strong uniqueness for the Euler alignment system", arxiv.2412.09590 (2024), accepted in Journal of Evolution Equations
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