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

06/12/2019

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by   Neelabja Chatterjee, et al.

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High-order accurate, 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.