Analysis of a High Order Finite Volume Scheme for the Vlasov-Poisson System

Roland Duclous (1) , Bruno Dubroca (1) , Francis Filbet (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 ICJ - Institut Camille Jordan

We propose a second order finite volume scheme to discretize the one-dimensional Vlasov-Poisson system with boundary conditions. For this problem, a rather general initial and boundary data lead to a unique solution with bounded variations but such a solution becomes discontinuous when the external voltage is large enough. We prove that the numerical approximation converges to the weak solution and show the efficiency of the scheme to simulate beam propagation with several particle species.

Domaines: Analyse numérique [math.NA]

Roland Duclous, Bruno Dubroca, Francis Filbet. Analysis of a High Order Finite Volume Scheme for the Vlasov-Poisson System. Discrete and Continuous Dynamical Systems - Series S, 2012, 5, pp.283-305. ⟨hal-00287630⟩