Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
Abstract
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by the scheme. The method is formally first-order accurate in space. A series of higher-order methods is also introduced. When these methods violate the invariant domain properties, they are corrected by a limiting technique that we call convex limiting. After limiting, the resulting methods satisfy all the invariant domain properties that are imposed by the user (see Theorem~7.24). A key novelty is that the bounds that are enforced on the solution at each time step are necessarily satisfied by the low-order approximation.
Keywords
Cite
@article{arxiv.1807.02563,
title = {Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems},
author = {Jean-Luc Guermond and Bojan Popov and Ignacio Tomas},
journal= {arXiv preprint arXiv:1807.02563},
year = {2019}
}