A Lax-Wendroff type theorem for unstructured quasiuniform grids
Abstract
A well-known theorem of Lax and Wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a.e. as the mesh parameter goes to zero, then the limit is a weak solution of the system. Moreover, if the scheme satisfies a discrete entropy inequality as well, the limit is an entropy solution. The original theorem applies to uniform Cartesian grids; this article presents a generalization for quasiuniform grids (with Lipschitz-boundary cells) uniformly continuous inhomogeneous numerical fluxes and nonlinear inhomogeneous sources. The added generality allows a discussion of novel applications like local time stepping, grids with moving vertices and conservative remapping. A counterexample demonstrates that the theorem is not valid for arbitrary non-quasiuniform grids.
Cite
@article{arxiv.math/0509331,
title = {A Lax-Wendroff type theorem for unstructured quasiuniform grids},
author = {Volker Elling},
journal= {arXiv preprint arXiv:math/0509331},
year = {2007}
}