Convergence of second-order, entropy stable methods for multi-dimensional conservation laws

Neelabja Chatterjee, Ulrik Skre Fjordholm

High-order accurate, $\textit{entropy stable}$ 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.

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