Publications

Publications of research papers, review papers - or conference contributions related to the SPP2410 priority program

2026

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 

 
Chertock, A., Herty, M., Kurganov, A., Lukáčová-Medvid’ová, M. (2026). Challenges in Stochastic Galerkin Methods for Nonlinear Hyperbolic Systems with Uncertainty. In: Morales de Luna, T., Boscarino, S., Frolkovič, P., Müller, L.O., Escalante, C. (eds) Advances in Nonlinear Hyperbolic Partial Differential Equations. ICIAM 2023. ICIAM2023 Springer Series, vol 7. Springer, Singapore. https://doi.org/10.1007/978-981-96-9087-9_4 
 
Janina Bender and Thomas Izgin and Philipp Öffner and Davide Torlo: "The Lax–Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws" Computers & Fluids Volume 304, 106885 (2026)
 
Gess, B., Gvalani, R.S. & Konarovskyi, V. Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent. Probab. Theory Relat. Fields 192, 1447–1515 (2025).
J. Conrad, S. Görtz, and M. Oberlack. “On the kinetic equations of elastic turbulence and their implications”. In: under consideration in Physical Review E. (2026)
 
S. Görtz, J. Conrad, D. Plümacher, and M. Oberlack. “Isotropic velocity probability density functions”. In: under consideration in ZAMM - Journal of Applied Mathematics and Mechanics (2026)
 
S. Görtz, J. Conrad, and M. Oberlack. “High-moment scaling laws of wall-bounded turbulent shear flows: Invariant solutions to the infinite multi-point moment equations”. In: under consideration in Physical Review Fluids (2026)
 
M. Oberlack, S. Görtz, S. Hoyas, P. Hollmann, and J. Conrad. “Arbitrary high-moment velocity statistics of wall-bounded shear flows: Extending the symmetry theory”. In: under consideration in Physical Review Letters (2026)
 
S. Görtz, L. De Broeck, P. Hollmann, and M. Oberlack. “Acoustic theory of compressible shear layers. Part 1. Power series solutions, equivalence transformations and instabilities”. In: under consideration in Journal of Fluid Mechanics (2026)
 
S. Görtz, L. De Broeck, P. Hollmann, and M. Oberlack. “Acoustic theory of compressible shear layers. Part 2. Wave scattering, resonant over reflection and wave absorption”. In: under consideration in Journal of Fluid Mechanics (2026)
 
Niklas Kolbe, Siegfried Müller and Aleksey Sikstel: "Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems", https://arxiv.org/abs/2601.11172 (2026)
 
B. Gess, R. S. Gvalani, and A. Martini: “Ergodicity of SPDEs with divergence-free transport noise”, arXiv:2601.22056 (2026)
 
Anika Beckers, Jan Friedrich: Monotone-based Numerical Schemes for Two-Dimensional Systems of Nonlocal Conservation Laws, arXiv:2601.20494 (2026)
 
Wittenstein, Collin and Marks, Vincent and Ricchiuto, Mario and Ranocha, Hendrik: "GPU-Accelerated Energy-Conserving Methods for the Hyperbolized Serre-Green-Naghdi Equations in 2D" arXiv:2601.02540 (2026)
 
Q Huang, C Rohde, R Zhang. Convergence of a two-parameter hyperbolic relaxation system toward the incompressible Navier-Stokes equations. 2026, arXiv:2601.19846
 
Thomas Eiter, Robert Lasarzik, Marcel Śliwiński: Existence and selection of solutions in the energy-variational framework with applications in fluid dynamics (2026) arXiv/2601.20455
 
Jan Giesselmann, Jens Keim, Fabio Leotta, Christian Rohde: "Justification of a Relaxation Approximation for the Navier-Stokes-Cahn-Hilliard System", arxiv.2601.18463 (2026)
 
Louis Petri, Sigrun Ortleb, Gunnar Birke, Christian Engwer, Hendrik Ranocha: "Domain-of-dependence-stabilized cut-cell discretizations of linear kinetic models with summation-by-parts properties", arxiv.2601.05817 (2026)
 
Jan Giesselmann, Philipp Öffner, Robert Sauerborn: "A Structure Preserving Finite Volume Scheme for the Navier-Stokes-Korteweg Equations" arxiv:2601.08498 (2026)
 
Joshua Vedral, Dmitri Kuzmin: "Cell-vertex WENO schemes with shock-capturing quadrature for high-order finite element discretizations of hyperbolic problems", arxiv:2601.16911 (2026)
 
Benjamin Gess, Robert Lasarzik: "Probabilistically Strong Solutions to Stochastic Euler Equations", arxiv:2601.22073 (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

Jan Giesselmann, Hendrik Ranocha: "Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions", SMAI J. Comput. Math (2026)

2025

Krupa, S.G., Székelyhidi, L. Contact Discontinuities for 2-D Isentropic Euler are Unique in 1-D but Wildly Non-unique Otherwise. Commun. Math. Phys. 406, 109 (2025). 
 
Simon Markfelder, Valentin Pellhammer: "Failure of the least action admissibility principle in the context of the compressible Euler equations", arxiv:2502.09292 (2025)
 
Shyam Sundar Ghoshal, Parasuram Venkatesh, Emil Wiedemann. A non-conservative, non-local approximation of the Burgers equation[J]. Networks and Heterogeneous Media, 2025, 20(4): 1061-1086. doi: 10.3934/nhm.2025046
 
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 
 
Lampert, Joshua and Wittenstein, Collin and Ranocha, Hendrik: "DispersiveShallowWater.jl: A Julia library of structure-preserving numerical methods for dispersive wave equations" Journal of Open Source Software, 10(116), 9361, https://doi.org/10.21105/joss.09361 (2025)
 
D. Breit, T. C. Moyo, A. Prohl &. J. Wichmann: "Mean Square Temporal error estimates for the two-dimensional stochastic Navier–Stokes equations with transport noise". IMA J. Num. Anal. (2025)
 
T. Crin-Barat, N. D. Nitti, S. Skondric, and A. Violini. Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness", Nonlinearity 38 (2025)
 
T. Crin-Barat, S. Skondric, and A. Violini. “Relative energy method for weak-strong uniqueness of the inhomogeneous Navier–Stokes equations far from vacuum”. J. Evol. Equ. 25.1 (2025), Paper No. 6 (2025)
 
Dumbser, M., Lukáčová-Medvid’ová, M. & Thomann, A.: "Convergence of a hyperbolic thermodynamically compatible finite volume scheme for the Euler equations" Numer. Math. (2025)
 
M. Anandan,   M.  Lukáčová - Medvid'ová,  S. V. Raghurama Rao:  An asymptotic preserving scheme satisfying entropy stability for the barotropic Euler system, 2025, SeMA Journal
 
Lukáčová-Medvid'ová, Mária; She, Bangwei; Yuan, Yuhuan: What is a limit of structure-preserving numerical methods for compressible flows? Numerical mathematics and advanced applications—ENUMATH 2023. Vol. 1, 17–33, Lect. Notes Comput. Sci. Eng., 153, Springer, Cham, [2025]
 
Lukáčová-Medvid'ová, Mária; She, Bangwei; Yuan, Yuhuan; Penalty method for the Navier–Stokes–Fourier system with Dirichlet boundary conditions: convergence and error estimates. Numer. Math. 157 (2025), no. 3, 1079–1132. 
 
Lukáčová-Medviďová, Mária; She, Bangwei; Yuan, Yuhuan; Convergence Analysis of the Monte Carlo Method for the Random Navier–Stokes–Fourier System. SIAM J. Numer. Anal. 63 (2025), no. 3, 1254–1280.
 
Feireisl, Eduard; Lukáčová - Medvid'ová, Mária; She, Bangwei; Yuan, Yuhuan: Error analysis of the Monte Carlo method for compressible magnetohydrodynamics. Math. Models Methods Appl. Sci. 35 (2025), no. 9, 2047–2097.
 

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

Michael Herty and Ferdinand Thein: On the relation between approaches for boundary feedback control of hyperbolic systems, 10.1016/j.ejcon.2025.101182, (2025)
 

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

Keim, Jens; Konan, Hasel; Rohde, Christian, A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow, ESAIM: ProcS Volume 78 (2025), https://doi.org/10.1051/proc/202578188
 
Beckers, A., & Kolbe N., The Lax–Friedrichs method in one-dimensional hemodynamics and its simplifying effect on boundary and coupling conditions. Computer Methods in Biomechanics and Biomedical Engineering, 1–14 (2025). https://doi.org/10.1080/10255842.2025.2532027
 

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

Barsukow, W., Kern, J., Klingenberg, C. L. Lechner, Analysis of the Multi-dimensional Semi-discrete Active Flux Method Using the Fourier Transform. Commun. Appl. Math. Comput. (2025). https://doi.org/10.1007/s42967-025-00512-3
 
Kuzmin, Dmitri, Lukáčová-Medvid’ová, Mária and Öffner, Philipp. "Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems" Journal of Numerical  Mathematics. (2025) https://doi.org/10.1515/jnma-2024-0123
 
J. Glaubitz, H. Ranocha, A. R. Winters, M. Schlottke-Lakemper, P. Öffner, G. J. Gassner - Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods, Journal of Computational Physics 529 (2025). https://doi.org/10.1016/j.jcp.2025.113841
 
Thein, F., Warnecke, G.,  Balance Laws and Transport Theorems for Flows with Singular Interfaces. In: Fuhrmann, J., Hömberg, D., Müller, W.H., Weiss, W. (eds) Advances in Continuum Physics. Advanced Structured Materials, vol 238. Springer, Cham. (2025). https://doi.org/10.1007/978-3-031-93918-1_9
 
Schwarz, Anna; Kempf, Daniel; Keim, Jens; Kopper, Patrick; Rohde, Christian; Beck, Andrea, Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows, Computers & Fluids 303 (2025). https://doi.org/10.1016/j.compfluid.2025.106874
Z. P. Adams, M. Engel, and R. S. Gvalani: “Separation of time scales in weakly interacting diffusions”, arXiv:2502.12881 (2025)
 
R. Chemnitz and D. Chemnitz: “Mixing at the Batchelor Scale for White-In-Time Flows”, arXiv:2512.04297 (2025)
 
M. G. Delgadino and R. S. Gvalani: “Sharp mean-field estimates for the repulsive log gas in any dimension”, arXiv:2506.22083 (2025)
 
N. Gerber, R. S. Gvalani, M. Hairer, G. A. Pavliotis, and A. Schlichting: “Formation of clusters and coarsening in weakly interacting diffusions”, arXiv:2510.17629 (2025)
 
B. Gess, R. S. Gvalani, and S. Hu: “Random dynamical systems for McKean–Vlasov SDEs via rough path theory”, arXiv:2507.02449 (2025)
 
Dmitri Kuzmin, Hennes Hajduk, Joshua Vedral: "A matrix-free convex limiting framework for continuous Galerkin methods with nonlinear stabilization", arxiv:2509.04673 (2025)
 
Rémi Abgrall, Philipp Öffner, Yongle Liu: "Some new properties of the PamPa scheme" arxiv:2508.17147 (2025)
 
Paola Goatin, Simone Göttlich, Fabian Ziegler: "A non-local model for heterogeneous material flow on conveyor belts", arxiv:2510.17500 (2025)
 
Marco Artiano, Oswald Knoth, Peter Spichtinger, Hendrik Ranocha: "Structure-Preserving High-Order Methods for the Compressible Euler Equations in Potential Temperature Formulation for Atmospheric Flows", arxiv:2509.10311 (2025)
 
Georgy Zinchenko, Jörg Schumacher: "Extending the Duchon-Robert framework for anomalous dissipation to compressible fluid flows", arxiv.2508.03401 (2025)
 
Thomas Eiter: "Solution concepts for a model of visco-elasto-plasticity with slight compressibility: arxiv.2512.17464 (2025)
 
Jens Schröder, Emil Wiedemann: "On the Vanishing Viscosity Limit for Inhomogeneous Incompressible Navier-Stokes Equations on Bounded Domains", arxiv2507.01642 (2025)
 
Šárka Nečasová, Tong Tang, Emil Wiedemann, Lu Zhu: "Energy Conservation and Vanishing Viscosity Limit for the Primitive Equations", arxiv2505.15658 (2025)
 
Christian Seis, Emil Wiedemann, Jakub Woźnicki: "Strong Convergence of Vorticities in the 2D Viscosity Limit on a Bounded Domain", arxiv.2406.05860 (2025)
 
Robert Lasarzik: "Energy-variational structure in evolution equations" , arxiv.2503.11438 (2025)
 
Amelie Porfetye and Zhuyan Tang and Shaoshuai Chu and Christiane Helzel and Maria Lukacova-Medvidova: New Fully Discrete Active Flux Methods with Truly Multi-Dimensional Evolution Operators and WENO Reconstruction, arXiv:2512.16359 (2025)
 
E. Feireisl, M. Lukacova-Medvidova: Well-posedness of the Euler system of gas dynamics, arXiv:2512.18267 (2025)
 
A. Babbar, V. Churavy, M. Schlottke-Lakemper, H. Ranocha: "Automatic differentiation for Lax-Wendroff-type discretizations", arXiv:2506.11719 (2025)
 
Tommaso Ruggeri, Ferdinand Thein, Qinghua Xiao: "Self-Similar Radially Symmetric Solutions of the Relativistic Euler Equations with Synge Energy" arxiv:2511.18971 (2025)
 
H. Ranocha, D. Ketcheson: "Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations" arxiv:2512.16352 (2025)
 
A. Babbar, H. Ranocha: "Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations" arxiv:2512.08611 (2025)
 
Jan Friedrich, Samala Rathan, Sanjibanee Sudha: "A note on the central-upwind scheme for nonlocal conservation laws“ arxiv:2512.01344 (2025)
 
Gennaro Ciampa, Tommaso Cortopassi, Gianluca Crippa, Raffaele D'Ambrosio, Stefano Spirito: "A priori error estimates for the $\theta$-method for the flow of nonsmooth velocity fields" arxiv:2506.02747 (2025)
 
Gianluca Crippa, Eliseo Luongo, Umberto Pappalettera: "Zero-noise selection and Large Deviations in $L^\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions"  arxiv:2506.06947 (2025)

Gianluca Crippa: "Introduction to the theory of mixing for incompressible flows" arXiv:2511.03360 (2025)

R. Boadi, D. Breit & T. C. Moyo: "Compressible Euler equations with transport noise" arXiv:2511.20131 (2025)
 
D. Breit, E. Feireisl, M. Hofmanova & P. B. Mucha: "Compressible fluids excited by space-dependent transport noise" arXiv:2504.10256 (2025)
 
M. Inversi and A. Violini: "Inhomogeneous incompressible Euler with codimension 1 singular structures" arXiv: 2412.09493 (2025) 
 
S. Skondric: "Existence and uniqueness of Leray-Hopf weak solution for the inhomogeneous 2D Navier–Stokes equations without vacuum" arXiv: 2504.16638 (2025)
 
E. Feireisl, , M. Lukacova-Medvidova, C. Yu: "Oscillatory approximations and maximum entropy principle for the Euler system of gas dynamic", arXiv:2505.02070 (2025)
 
E. Feireisl, , A. Jüngel, M. Lukacova-Medvidova: "Maximal dissipation and well-posedness of the Euler system of gas dynamic", arXiv:2501.05134 (2025)
 
A. Chertock, M. Herty, A. Ishakov,  A. Ishakova, A. Kurganov,  M. Lukacova-Medvidova:  "Numerical study of random Kelvin-Helmholtz instability", arXiv:2511.00008 (2025)
 
M. Lukacova-Medvidova,  F. Thein, G. Warnecke, Y. Yuan: "A note on relations between convexity and concavity of thermodynamic functions", arXiv:2510.24440 (2025)
 
Matthias Sroczinski, Kevin Zumbrun: "Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems ", arXiv:2510.09287 (2025)
 
Sebastian Bleecke, Abhijit Biswas, David I. Ketcheson, Hendrik Ranocha, Jochen Schutz: "Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation", arXiv:2511.10044 (2025)
 
Aaron Brunk, Jan Giesselmann, Tabea Tscherpel: "A posteriori existence of strong solutions to the Navier-Stokes equations in 3D", 2025, arXiv:2509.25105
 
Andreas Dedner, Jan Giesselmann, Kiwoong Kwon, Tristan Pryer: "A posteriori analysis for nonlinear convection-diffusion systems", 2025, arXiv:2510.09449
 
Hendrik Ranocha, David I. Ketcheson: High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization", 2025, arXiv:2510.14335
 
Marc Hoffmann, Jan Giesselmann: "A posteriori existence for the Keller-Segel model via a finite volume scheme", 2025, arXiv:2509.17710
 
Montanaro, Veronica; Netterdon, Lukas; Torrilhon, Manuel; Gorji, Hossein: Fisher entropic Fokker-Planck model of monatomic rarefied gas flows, 2025, arXiv:2509.06610
 
Keim, Jens; Schwarz, Anna; Kopper, Patrick; Blind, Marcel; Rohde, Christian; Beck, Andrea: Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes, 2025, arXiv:2507.04334
 
Schwarz, Anna; Keim, Jens; Rohde Chrisitan; Beck, Andrea: Entropy stable shock capturing for high-order DGSEM on moving meshes, 2025, arXiv:2503.23237
 
Qian Huang, Christian Rohde: "Numerical approximations to statistical conservation laws for scalar hyperbolic equations", arXiv:2509.05039 (2025)
 
Qian Huang, Christian Rohde: Statistical conservation laws for scalar model problems: Hierarchical evolution equations. arXiv:2508.15359 (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)

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", submitted,  https://arxiv.org/abs/2505.23144 (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)

Stefano Abbate, Luigi C. Berselli, Gianluca Crippa, Stefano Spirito: "Convergence of the Euler-Voigt equations to the Euler equations in two dimensions", Journal of Nonlinear Science, arxiv:2503.01270 (2025)
 
Chu, S., M. Herty, M. Lukacov a-Medvid’ova, and Y. Zhou: Solving random hyperbolic conservation laws using linear programming, arXiv:2501.10104, accepted to SIAM J. Sci. Comput. 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

M. Lukacova-Medvidova,  S. Schneider: "Estimatable variation neural networks and their application to ODEs and scalar hyperbolic conservation laws", arXiv:2409.08909 (2024)
 
E. Feireisl, , M. Lukacova-Medvidova,  H. Mizerova, C. Yu; "Monte Carlo method and the random isentropic Euler system", arXiv:2404.11983 (2024)
 
Maren Hantke, Siegfried Müller, Aleksey Sikstel, Ferdinand Thein: A survey on isothermal and isentropic Baer-Nunziato-type models, https://arxiv.org/abs/2407.06919, (2024)
 

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

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