An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems

Abstract

We develop a stable split-form discontinuous Galerkin spectral element method for the solution of variable coefficient linear hyperbolic systems of conservation laws. In our presentation, we start with the simplest problem and introduce complexity as we progress. We begin with the approximation of scalar conservation laws in one space dimension. We then extend the derivation to hyperbolic systems. Finally, we approximate the two-dimensional problem. Numerical experiments are performed to compare the approximations.