High order entropy stable discontinuous Galerkin schemes in a space-time computational framework
In this paper we present a space-time computational framework for solution of nonlinear hyperbolic systems of conservation laws. The framework is based on a previously proposed space-time discontinuous Galerkin discretization, realized in terms of entropy variables. Building on previous stability and convergence analysis, the main aim of the present paper is to address the increased complexity of the high-order implicit space-time formulation. We propose a time-marching scheme of the tent-pitching type, maintaining the implicit nature of the solution algorithm, as well as high order temporal accuracy, while avoiding global space-time coupling of the degrees of freedom. The algorithm is introduced and numerical experiments for different linear and nonlinear test cases are presented.
