1 citations · 1 across the 5 of their papers we have counts for
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Well-balanced second-order approximation of the compressible atmospheric Euler equations
Crystal Farris, Matthias Maier, Eric J. Tovar
We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to rest st…
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…
A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement
Jake Harmon, Martin Kronbichler, Matthias Maier +1
We propose a rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets…
A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations
Jean-Luc Guermond, Matthias Maier, Eric Tovar
We introduce a high-order space-time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP) and well-balanced with respect to rest stat…
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…
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…