Class of space-time entropy stable dg schemes for systems of convection–diffusion

Abstract

In this work, we present a family of entropy stable discontinuous Galerkin methods for systems of convection–diffusion with nonlinear convective and viscous fluxes. The discretization presented here is based on a mixed formulation and is designed to preserve entropy stability of an already existing entropy stable discretization for a hyperbolic system of conservation laws. The fully discrete version of the entropy stability is proven in the framework of space–time formulation with variants of several known schemes, including the method of Bassi–Rebay and symmetric interior penalty method.