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Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
Mathematics and Statistics Faculty Publications and Presentations
  • Bernardo Cockburn, University of Minnesota - Twin Cities
  • Jay Gopalakrishnan, Portland State University
  • Raytcho Lazarov, Texas A & M University - College Station
Document Type
Publication Date
  • Finite element method,
  • Hybridization,
  • Elliptic functions,
  • Galerkin methods,
  • Boundary element methods
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, continu- ous Galerkin, non-conforming 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.

This is the author’s version of a work that was accepted for publication in SIAM Journal on Numerical Analysis. A definitive version was subsequently published in SIAM Journal on Numerical Analysis, 2009. Vol. 47 Issue 2, p. 1319-1365.

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Citation Information
Bernardo Cockburn, Jay Gopalakrishnan and Raytcho Lazarov. "Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems" (2009)
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