A relaxation scheme for conservation laws with a discontinuous coefficient. - Kenneth H. Karlsen; Christian Klingenberg; Nils Henrik Risebro (Math. Comput., 2004)

Numerical comparison of Riemann solvers for astrophysical hydrodynamics. - Christian Klingenberg; Wolfram Schmidt; Knut Waagan (J. Comput. Phys., 2007)

A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework. - François Bouchut; Christian Klingenberg; Knut Waagan (Numerische Mathematik, 2007)

A multiwave approximate Riemann solver for ideal MHD based on relaxation II: numerical implementation with 3 and 5 waves. - François Bouchut; Christian Klingenberg; Knut Waagan (Numerische Mathematik, 2010)

A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests. - Knut Waagan; Christoph Federrath; Christian Klingenberg (J. Comput. Phys., 2011)

A Second Order Well-Balanced Finite Volume Scheme for Euler Equations with Gravity. - Praveen Chandrashekar; Christian Klingenberg (SIAM J. Sci. Comput., 2015)

Well-balanced schemes to capture non-explicit steady states: Ripa model. - Vivien Desveaux; Markus Zenk; Christophe Berthon; Christian Klingenberg (Math. Comput., 2016)

Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes. - Praveen Chandrashekar; Christian Klingenberg (SIAM J. Numer. Anal., 2016)

Well-Balanced Unstaggered Central Schemes for the Euler Equations with Gravitation. - Rony Touma; Ujjwal Koley; Christian Klingenberg (SIAM J. Sci. Comput., 2016)

Simulating Turbulence Using the Astrophysical Discontinuous Galerkin Code TENET. - Andreas Bauer; Kevin Schaal; Volker Springel; Praveen Chandrashekar; Rüdiger Pakmor; Christian Klingenberg (Software for Exascale Computing, 2016)

A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics. - Wasilij Barsukow; Philipp V. F. Edelmann; Christian Klingenberg; Fabian Miczek; Friedrich K. Röpke (J. Sci. Comput., 2017)

An Arbitrary Lagrangian-Eulerian Local Discontinuous Galerkin Method for Hamilton-Jacobi Equations. - Christian Klingenberg; Gero Schnücke; Yinhua Xia (J. Sci. Comput., 2017)

Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension. - Christian Klingenberg; Gero Schnücke; Yinhua Xia (Math. Comput., 2017)

A Fokker-Planck approach to control collective motion. - Souvik Roy; Mario Annunziato; Alfio Borzì; Christian Klingenberg (Comput. Optim. Appl., 2018)

Multilevel Monte Carlo Finite Volume Methods for Random Conservation Laws with Discontinuous Flux. - Jayesh Badwaik; Nils Henrik Risebro; Christian Klingenberg (CoRR, 2019)

An all speed second order IMEX relaxation scheme for the Euler equations. - Andrea Thomann; Markus Zenk; Gabriella Puppo; Christian Klingenberg (CoRR, 2019)

Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations. - Jayesh Badwaik; Praveen Chandrashekar; Christian Klingenberg (CoRR, 2019)

The Active Flux Scheme on Cartesian Grids and Its Low Mach Number Limit. - Wasilij Barsukow; Jonathan Hohm; Christian Klingenberg; Philip L. Roe (J. Sci. Comput., 2019)

On the Low Mach Number Limit for the Compressible Euler System. - Eduard Feireisl; Christian Klingenberg; Simon Markfelder (SIAM J. Math. Anal., 2019)

Arbitrary Order Finite Volume Well-Balanced Schemes for the Euler Equations with Gravity. - Christian Klingenberg; Gabriella Puppo; Matteo Semplice (SIAM J. Sci. Comput., 2019)

Zero relaxation time limits to isothermal hydrodynamic model for semiconductor. - Changfeng Xue; Christian Klingenberg; Yun-guang Lu; Jin-jun Zhang (Appl. Math. Lett., 2020)

Entropy Stable Numerical Fluxes for Compressible Euler Equations which are Suitable for All Mach Numbers. - Jonas P. Berberich; Christian Klingenberg (CoRR, 2020)

Exact solution and the multidimensional Godunov scheme for the acoustic equations. - Wasilij Barsukow; Christian Klingenberg (CoRR, 2020)

High order discretely well-balanced finite volume methods for Euler equations with gravity - without any à priori information about the hydrostatic solution. - Jonas P. Berberich; Roger Käppeli; Praveen Chandrashekar; Christian Klingenberg (CoRR, 2020)

Using the Navier-Cauchy equation for motion estimation in dynamic imaging. - Bernadette N. Hahn; Melinda-Loren Kienle-Garrido; Christian Klingenberg; Sandra Warnecke (CoRR, 2020)

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes. - Elena Gaburro; Walter Boscheri; Simone Chiocchetti; Christian Klingenberg; Volker Springel; Michael Dumbser (J. Comput. Phys., 2020)

An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity. - Andrea Thomann; Gabriella Puppo; Christian Klingenberg (J. Comput. Phys., 2020)

Kinetic/Fluid Micro-Macro Numerical Scheme for a Two Component Gas Mixture. - Anaïs Crestetto; Christian Klingenberg; Marlies Pirner (Multiscale Model. Simul., 2020)

Nonuniqueness of Admissible Weak Solution to the Riemann Problem for the Full Euler System in Two Dimensions. - Hind Al Baba; Christian Klingenberg; Ondrej Kreml; Václav Mácha 002; Simon Markfelder (SIAM J. Math. Anal., 2020)

EXAMAG: Towards Exascale Simulations of the Magnetic Universe. - Volker Springel; Christian Klingenberg; Rüdiger Pakmor; Thomas Guillet; Praveen Chandrashekar (Software for Exascale Computing, 2020)

Global entropy solutions for systems modelling polymer flooding in enhanced oil recovery. - Yun-guang Lu; Changfeng Xue; Christian Klingenberg (Appl. Math. Lett., 2021)

Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting. - Kathrin Hellmuth; Christian Klingenberg; Qin Li 007; Min Tang 002 (Comput., 2021)

Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers. - Philipp V. F. Edelmann; L. Horst; Jonas P. Berberich; R. Andrassy; J. Higl; Christian Klingenberg; Friedrich K. Röpke (CoRR, 2021)

A low Mach two-speed relaxation scheme for the compressible Euler equations with gravity. - Claudius Birke; Christophe Chalons; Christian Klingenberg (CoRR, 2021)

Reconstruction of the Emission Coefficient in the Nonlinear Radiative Transfer Equation. - Christian Klingenberg; Ru-Yu Lai; Qin Li 007 (SIAM J. Appl. Math., 2021)

On the Active Flux Scheme for Hyperbolic PDEs with Source Terms. - Wasilij Barsukow; Jonas P. Berberich; Christian Klingenberg (SIAM J. Sci. Comput., 2021)

Global solutions of the Cauchy problem to Euler-Poisson equations of two-carrier types. - Silu Yin; Xianting Wang; Yun-guang Lu; Christian Klingenberg (Appl. Math. Lett., 2022)

A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors. - Giovanni Leidi; Claudius Birke; R. Andrassy; J. Higl; Philipp V. F. Edelmann; G. Wiest; Christian Klingenberg; Friedrich K. Röpke (CoRR, 2022)

A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations. - Hubert Baty; Florence Drui; Philippe Helluy; Emmanuel Franck; Christian Klingenberg; Lukas Thanhäuser (Appl. Math. Comput., 2023)

Numerical reconstruction of the kinetic chemotaxis kernel from macroscopic measurement, wellposedness and illposedness. - Kathrin Hellmuth; Christian Klingenberg; Qin Li 007; Min Tang 002 (CoRR, 2023)

The Active Flux method for the Euler equations on Cartesian grids. - Rémi Abgrall; Wasilij Barsukow; Christian Klingenberg (CoRR, 2023)

Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency. - Jeffrey R. Haack; Cory D. Hauck; Christian Klingenberg; Marlies Pirner; Sandra Warnecke (J. Comput. Phys., 2023)

Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model. - Luis Kaiser; Richard Tsai 001; Christian Klingenberg (CoRR, 2024)

Active flux methods for hyperbolic conservation laws - flux vector splitting and bound-preservation: One-dimensional case. - Junming Duan; Wasilij Barsukow; Christian Klingenberg (CoRR, 2024)

A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case. - Yu-Chen Cheng; Christian Klingenberg; Rony Touma (CoRR, 2024)

A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case. - Yu-Chen Cheng; Christian Klingenberg; Rony Touma (CoRR, 2024)

Active flux methods for hyperbolic conservation laws - flux vector splitting and bound-preservation: Two-dimensional case. - Junming Duan; Wasilij Barsukow; Christian Klingenberg (CoRR, 2024)

Preserving positivity of Gauss-Newton Hessian through random sampling. - Kathrin Hellmuth; Christian Klingenberg; Qin Li 007 (CoRR, 2024)

A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation. - Lena Baumann; Lukas Einkemmer; Christian Klingenberg; Jonas Kusch (CoRR, 2024)

Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform. - Wasilij Barsukow; Janina Kern; Christian Klingenberg; Lisa Lechner (CoRR, 2024)

Energy Stable and Conservative Dynamical Low-Rank Approximation for the Su-Olson Problem. - Lena Baumann; Lukas Einkemmer; Christian Klingenberg; Jonas Kusch (SIAM J. Sci. Comput., 2024)

A Well-Balanced Semi-implicit IMEX Finite Volume Scheme for Ideal Magnetohydrodynamics at All Mach Numbers. - Claudius Birke; Walter Boscheri; Christian Klingenberg (J. Sci. Comput., 2024)

Kinetic Chemotaxis Tumbling Kernel Determined from Macroscopic Quantities. - Kathrin Hellmuth; Christian Klingenberg; Qin Li 007; Min Tang 002 (SIAM J. Math. Anal., 2024)

Reconstructing the Kinetic Chemotaxis Kernel Using Macroscopic Data: Well-Posedness and Ill-Posedness. - Kathrin Hellmuth; Christian Klingenberg; Qin Li 007; Min Tang 002 (SIAM J. Appl. Math., 2025)

Active Flux Methods for Hyperbolic Conservation Laws - Flux Vector Splitting and Bound-Preservation. - Junming Duan; Wasilij Barsukow; Christian Klingenberg (SIAM J. Sci. Comput., 2025)

An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem. - Lena Baumann; Lukas Einkemmer; Christian Klingenberg; Jonas Kusch (CoRR, 2025)

A generalized Active Flux method of arbitrarily high order in two dimensions. - Wasilij Barsukow; Praveen Chandrashekar; Christian Klingenberg; Lisa Lechner (CoRR, 2025)

A Semi-discrete Active Flux Method for the Euler Equations on Cartesian Grids. - Rémi Abgrall; Wasilij Barsukow; Christian Klingenberg (J. Sci. Comput., 2025)

Active flux for ideal magnetohydrodynamics: A positivity-preserving scheme with the Godunov-Powell source term. - Junming Duan; Praveen Chandrashekar; Christian Klingenberg (CoRR, 2025)

An adaptive dynamical low-rank optimizer for solving kinetic parameter identification inverse problems. - Lena Baumann; Lukas Einkemmer; Christian Klingenberg; Jonas Kusch (CoRR, 2025)

Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators. - Wasilij Barsukow; Christian Klingenberg; Lisa Lechner; Jan Nordström; Sigrun Ortleb; Hendrik Ranocha (CoRR, 2025)

An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling. - Junming Duan; Wasilij Barsukow; Christian Klingenberg (CoRR, 2025)