Unified hybridization of discont inuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems

Bernardo Cockburn, Jayadeep Gopalakrishnan, Raytcho Lazarov

Research output: Contribution to journalArticlepeer-review

572 Scopus citations

Abstract

We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continuous Galerkin, nonconforming, and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements. Since the associated matrix is sparse, symmetric, and positive definite, these methods can be efficiently implemented. Moreover, the framework allows, in a single implementation, the use of different methods in different elements or subdomains of the computational domain, which are then automatically coupled. Finally, the framework brings about a new point of view, thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques, as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom.

Original languageEnglish (US)
Pages (from-to)1319-1365
Number of pages47
JournalSIAM Journal on Numerical Analysis
Volume47
Issue number2
DOIs
StatePublished - 2009

Keywords

  • Continuous methods
  • Discontinuous Galerkin methods
  • Elliptic problems
  • Hybrid methods
  • Mixed methods

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