Convergence des méthodes particulaires renormalisées pour les systèmes de Friedrichs

Abstract

We present a study of the renormalized particle scheme. Renormalization is a tool introduced in order to alleviate the SPH particle methods' lack of consistency. A conservative scheme, the weak renormalized scheme, is derived from the general conservation laws weak formulation. We apply this scheme to Friedrichs systems. The weak renormalized scheme being unstable, we introduce a numerical viscosity before applying an explicit Euler time discretization, and thus construct the numerical scheme whose convergence in L 2 norm is studied. To cite this article: N. Lanson, J.-P. Vila, C. R. Acad. Sci. Paris, Ser. I 340 (2005).