Convergence of second-order, entropy stable methods for multi-dimensional conservation laws
Numerical Analysis
2019-06-13 v1 Numerical Analysis
Abstract
High-order accurate, numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space dimensions. In this paper we show how the entropy stability of one such method yields a (weak) bound on oscillations, and using compensated compactness we prove convergence to a weak solution satisfying at least one entropy condition.
Cite
@article{arxiv.1906.05115,
title = {Convergence of second-order, entropy stable methods for multi-dimensional conservation laws},
author = {Neelabja Chatterjee and Ulrik Skre Fjordholm},
journal= {arXiv preprint arXiv:1906.05115},
year = {2019}
}