An extended Galerkin analysis for elliptic problems

Qingguo Hong, Shuonan Wu, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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, uh, ph, ŭh and p⌣ h, where uh and ph are for approximation of u and p = −α∇u inside each element, and ŭh and p⌣ h are for approximation of residual of u and p · n on the boundary of each element. The resulting 4-field discretization is proved to satisfy two types of inf-sup conditions that are uniform with respect to all discretization and penalization parameters. As 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.
Original languageEnglish (US)
Pages (from-to)2141-2158
Number of pages18
JournalScience China Mathematics
Issue number9
StatePublished - Sep 1 2021
Externally publishedYes


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