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

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