Enhanced convergence estimates for semi-lagrangian schemes Application to the Vlasov-Poisson equation

Frédérique Charles (1) , Bruno Després (1) , Michel Mehrenberger (2, 3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 IRMA - Institut de Recherche Mathématique Avancée
3 CALVI - Scientific computation and visualization

We prove enhanced error estimates for high order semi-lagrangian discretizations of the Vlasov-Poisson equation. It provides new insights into optimal numerical strategies for the numerical solution of this problem. The new error estimate is based on advanced error estimates for semi-lagrangian schemes, also equal to shifted Strang's schemes, for the discretization of the advection equation.

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

Frédérique Charles, Bruno Després, Michel Mehrenberger. Enhanced convergence estimates for semi-lagrangian schemes Application to the Vlasov-Poisson equation. SIAM Journal on Numerical Analysis, 2011, ⟨10.1137/110851511⟩. ⟨inria-00629081⟩