Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson EquationsReport as inadecuate




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1 IRMA - Institut de Recherche Mathématique Avancée 2 CALVI - Scientific computation and visualization IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l-Image, de l-Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine

Abstract : The Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson-s equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky CK procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained.

Mots-clés : semi-Lagrangien schéma numérique convergence Vlasov





Author: Thomas Respaud - Eric Sonnendrücker -

Source: https://hal.archives-ouvertes.fr/



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