An extended Galerkin analysis for elliptic problems

作     者：Qingguo Hong Shuonan Wu Jinchao Xu Qingguo Hong;Shuonan Wu;Jinchao Xu

作者机构：Department of MathematicsPennsylvania State UniversityUniversity ParkPA16802USA School of Mathematical SciencesPeking UniversityBeijing100871China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2021年第64卷第9期

页      面：2141-2158页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by Center for Computational Mathematics and Applications,The Pennsylvania State University supported by National Natural Science Foundation of China(Grant No.11901016) the startup grant from Peking University supported by National Science Foundation of USA(Grant No.DMS-1522615) 

主　　题：finite element method extended Galerkin analysis unified study 

摘      要：A general analysis framework is presented in this paper for many different types of finite element methods(including various discontinuous Galerkin methods).For the second-order elliptic equation-div(α▽u)=f,this framework employs four different discretization variables,u_(h),p_(h),u_(h)and p_(h),where u_(h)and p_(h)are for approximation of u and p=-α▽u inside each element,and u_(h)and p_(h)are for approximation of the residual of u and p·n on the boundary of each *** resulting 4-field discretization is proved to satisfy two types of inf-sup conditions that are uniform with respect to all discretization and penalization *** a result,many existing finite element and discontinuous Galerkin methods can be analyzed using this general framework by making appropriate choices of discretization spaces and penalization parameters.