UNIFORM STABILITY AND ERROR ANALYSIS FOR SOME DISCONTINUOUS GALERKIN METHODS

• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 283-310
• 页数: 28页
• 语种: 英文
• DOI: 10.4208/jcm.2003-m2018-0223

摘要

In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.