Consistency results for the dual-wind discontinuous Galerkin method

Abstract

This paper further analyzes the dual-wind discontinuous Galerkin (DWDG) method for approximating Poisson’s problem by directly examining the relationship between the Laplacian and the underlying discrete Laplacian. DWDG methods are derived from the DG differential calculus framework that defines discrete differential operators to replace continuous differential operators. We establish a priori error estimates for the DWDG approximation of Δ. Since the DWDG method does not satisfy a Galerkin orthogonality condition, we also explore the relationship between the DWDG approximation and the Ritz projection defined to satisfy an exact Galerkin orthogonality condition linked to the DWDG method. Numerical experiments are provided to validate the theoretical results.