Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

Qingguo Hong, Jinchao Xu

Published 2018-05-22Version 1

In this paper, we prove two types of uniform stability results for some discontinuous Galerkin methods. Under the properly defined norms and the choice of commonly used spaces, we establish the uniform stability for both hybrid discontinuous Galerkin and weak Galerkin methods, which are uniformly stable with respect to stabilization and discretization parameters.Based on these uniform stability results, we also provide the uniformly optimal error estimates with respect to the stabilization parameters in the paper.