An optimal-order error estimate for the discontinuous Galerkin method

Abstract

In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in R 2 {R^2} , the method is shown to converge at a rate O ( h n + 1 ) O({h^{n + 1}}) when applied with nth degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.