Stability of finite volume schemes for hyperbolic systems in two space dimensions

Jean-François Coulombel (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 SIMPAF - SImulations and Modeling for PArticles and Fluids

We study the stability of finite volume schemes for symmetric hyperbolic systems in two space dimensions, with the Lax-Friedrichs flux. We first show a sufficient condition for the L2-stability of the scheme on a general triangulation. Then we show that this stability condition can be improved when the triangulation is composed of equilateral triangles.

Mots clés: Lax-Friedrichs flux; Hyperbolic systems; finite volume schemes; stability; Lax-Friedrichs flux.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jean-François Coulombel. Stability of finite volume schemes for hyperbolic systems in two space dimensions. 2006. ⟨hal-00020015v1⟩