Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method

Abstract

An adaptive multi-penalty discontinuous Galerkin method (AMPDG) for the diffusion problem is considered. Convergence and quasi-optimality of the AMPDG are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra works is done to overcome the difficulties caused by the additional penalty terms.