Performance of Discontinuous Galerkin Methods for Elliptic PDEs

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