TY - JOUR
T1 - A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems
AU - Sun , Zhiyuan
AU - Liu , Jun
AU - Wang , Pei
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 729
EP - 747
PY - 2020
DA - 2020/04
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0193
UR - https://global-sci.org/intro/article_detail/aamm/16421.html
KW - Convection-diffusion problem, polygonal mesh, discontinuous Galerkin method, patch reconstruction.
AB - <p style="text-align: justify;">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.</p>