Convergence of a Semi-Lagrangian Scheme for the One-Dimensional Vlasov--Poisson System

A semi-Lagrangian scheme is proposed for solving the periodic one-dimensional Vlasov--Poisson system in phase space on unstructured meshes. The distribution function f(t,x,v) and the electric field E(t,x) are shown to converge to the exact solution values in the $L^{\infty}$ norm. The rate of convergence is in O(h4/3 ).