An extended Galerkin analysis for elliptic problems

Qingguo Hong, Shuonan Wu, Jinchao Xu

Research output: Contribution to journalArticlepeer-review


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)
JournalScience China Mathematics
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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