Superconvergence Properties of Discontinuous Galerkin Methods for Two-Point Boundary Value Problems

Abstract

Three discontinuous Galerkin methods (SIPG, NIPG, DG) are considered for solving a one-dimensional elliptic problem. Superconvergence for the error at the interior node points and the derivative of the error at Gauss points are considered. All theoretical results obtained in the paper are supported by the results of numerical experiments.