4 papers
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…
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…