3 papers
math.NA2025
Structure-preserving finite-element approximations of the magnetic Euler-Poisson equations
Jordan Hoffart, Matthias Maier, John N. Shadid +1
We develop a structure-preserving numerical discretization for the electrostatic Euler-Poisson equations with a given magnetic field. Our focus is on the efficient solution of prob…
math.NA2024
Graph-based methods for hyperbolic systems of conservation laws using discontinuous space discretizations
Martin Kronbichler, Matthias Maier, Ignacio Tomas
We present a graph-based numerical method for solving hyperbolic systems of conservation laws using discontinuous finite elements. This work fills important gaps in the theory as w…
math.NA2023
First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system
Jean-Luc Guermond, Matthias Maier, Bojan Popov +2
The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to…