A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems

Abstract

In this article, we apply the discontinuous Galerkin method by patch reconstruction for solving convection-diffusion problems. The proposed method is highly efficient that it uses only one degree of freedom per element to achieve higher order approximation. It also enjoys the implementation flexibility on the general polygonal meshes. A priori error estimates of energy norm is devised. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.