Volume 54, Number 4, July-August 2020
|Page(s)||1415 - 1428|
|Published online||18 June 2020|
Convergence of second-order, entropy stable methods for multi-dimensional conservation laws
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern 0316 Oslo, Norway
Accepted: 10 December 2019
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, which is semi-discrete in time, yields a (weak) bound on oscillations. Under the assumption of L∞-boundedness of the approximations we use compensated compactness to prove convergence to a weak solution satisfying at least one entropy condition.
Mathematics Subject Classification: 35L65 / 65M12 / 65M08
Key words: Multi-dimensional conservation laws / finite volume methods / TECNO scheme / entropy stability
© EDP Sciences, SMAI 2020
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