We prove the convergence of discontinuous Galerkin approximations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials in velocity. To obtain stability properties, we introduce a suitable weighted L2 space, with a time dependent weight, and first prove global stability for the weighted L2 norm and propagation of regularity. Then we prove error estimates between the numerical solution and the smooth solution to the Vlasov-Poisson system.

Professor Francis Filbet is a full professor in applied mathematics at Université Paul Sabatier, Toulouse III, France. He obtained his PhD degree in applied mathematics in Université Henri Poincaré, Nancy I, in 2001, and obtained his Habilitation degree in Université Paul Sabatier, Toulouse III in 2005.  He used to be a professor of applied mathematics at Université Claude Bernard, Lyon I from 2006 to 2015. His research interests are numerical algorithms, scientific computing, partial differential equations, kinetic theory. Their applications are in rarefied gas dynamics, plasma physics, collective behavior in biology.