Relative entropy for the finite volume approximation of strong solutions to systems of conservation laws
Résumé
We study in this paper the finite volume approximation of strong solutions to systems of conservation laws. We derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical $h^{1/2}$ estimate under a $BV$ assumption on the numerical approximation.
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