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20232026
most citedA high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations

1 citations · 1 across the 5 of their papers we have counts for

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6 papers · 1 filter

math.NA2026

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…

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.NA2025

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…

math.NA2024★ 1 cited

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…

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…