Finite volume schemes and Lax-Wendroff consistency

2021/06/11 by Eymard, R, Gallouët, T, Herbin, R +1 · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2106.06380

Abstract

We present a (partial) historical summary of the mathematical analysis of finite differences and finite volumes methods, paying a special attention to the Lax-Richtmyer and Lax-Wendroff theorems. We then state a Lax-Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions.

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

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