Performance of discontinuous Galerkin methods for elliptic PDE's

Abstract

In this paper, we compare the performance of the main discontinuous Galerkin (DG) methods for elliptic partial differential equations on a model problem. Theoretical estimates of the condition number of the stiffness matrix are given for DG methods whose bilinear form is symmetric, which are shown to be sharp numerically. Then, the efficiency of the methods in the computation of both the potential and its gradient is tested on unstructured triangular meshes.