A unified study of continuous and discontinuous Galerkin methods

Qingguo Hong, Fei Wang, Shuonan Wu, Jinchao Xu

Research output: Contribution to journalReview article

10 Scopus citations

Abstract

A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid FEMs, discontinuous Galerkin (DG) methods, hybrid discontinuous Galerkin (HDG) methods and weak Galerkin (WG) methods. Both HDG and WG are shown to admit inf-sup conditions that hold uniformly with respect to both mesh and penalization parameters. In addition, by taking the limit of the stabilization parameters, a WG method is shown to converge to a mixed method whereas an HDG method is shown to converge to a primal method. Furthermore, a special class of DG methods, known as the mixed DG methods, is presented to fill a gap revealed in the unified framework.

Original languageEnglish (US)
JournalScience China Mathematics
Volume62
Issue number1
DOIs
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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