3 papers
math.NA2026
Stability analysis of Arbitrary-Lagrangian-Eulerian ADER-DG methods on classical and degenerate spacetime geometries
Mauro Bonafini, Davide Torlo, Elena Gaburro
In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classic…
math.NA2026
Flux-Balanced Patankar-type Schemes for the Compressible Euler Equations
Thomas Izgin, Andreas Meister, Chi-Wang Shu +1
Positivity preservation of key physical quantities in the context of fluid flows, such as density and internal energy, is an essential property of a numerical scheme as otherwise t…
math.NA2025
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Ãffner +1
For hyperbolic conservation laws, the famous Lax-Wendroff theorem delivers sufficient conditions for the limit of a convergent numerical method to be a weak (entropy) solution. Thi…