Conservative discontinuous Galerkin methods for the kinetic Fokker-Planck equation

Abstract

We consider the kinetic Fokker-Planck equation, a simplified model of the Vlasov-Landau equation, that describes collisions in plasma. This diffusion-type equation exhibits numerous noteworthy properties. One such property is the conservation of mass, momentum and energy. The numerical methods in this thesis, namely the local and recovery discontinuous Galerkin methods for diffusion-type equations, maintain this over large and truncated domains. Employing these methods results in stability results that fall in line with theoretical expectations. However, the findings also include unexpected convergence and asymptotic behaviors, which prompt further investigation.