Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems

Abstract

We develop dissipative, energy-stable difference methods for linear first-order hyperbolic systems by applying an upwind, discontinuous Galerkin construction of derivative matrices to a space of discontinuous piecewise polynomials on a structured mesh. The space is spanned by translates of a function spanning multiple cells, yielding a class of implicit difference formulas of arbitrary order. We examine the properties of the method, including the scaling of the derivative operator with method order, and demonstrate its accuracy for problems in one and two space dimensions.