On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General Meshes

2019/06/07 by Gallouët, Thierry, Herbin, R., Latché, J. -C · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1906.02973

Abstract

The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal regularity assumptions for the mesh. As in the seminal Lax-Wendroff paper, our approach relies on a discrete integration by parts of the weak formulation of the scheme. This makes a discrete gradient of the test function appear, and the central argument for the scheme consistency is to remark that this discrete gradient is convergent in L ∞ weak .

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• The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws

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