Structure preserving numerical methods for the Vlasov equation

To preserve a number of physically relevant invariants is a major concern when considering long time integration of the Vlasov equation. In the present work we consider the semi-Lagrangian discontinuous Galerkin method for the Vlasov-Poisson system. We discuss the performance of this method and compare it to cubic spline interpolation, where appropriate. In addition, numerical simulations for the two-stream instability are shown.