Convergence of second-order, entropy stable methods for multi-dimensional conservation laws
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 4, pp. 1415-1428.

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.

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DOI : 10.1051/m2an/2019090
Classification : 35L65, 65M12, 65M08
Mots-clés : Multi-dimensional conservation laws, finite volume methods, TECNO scheme, entropy stability 
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     author = {Chatterjee, Neelabja and Fjordholm, Ulrik Skre},
     title = {Convergence of second-order, entropy stable methods for multi-dimensional conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1415--1428},
     publisher = {EDP-Sciences},
     volume = {54},
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Chatterjee, Neelabja; Fjordholm, Ulrik Skre. Convergence of second-order, entropy stable methods for multi-dimensional conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 4, pp. 1415-1428. doi : 10.1051/m2an/2019090. http://www.numdam.org/articles/10.1051/m2an/2019090/

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