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.
Cockburn, B.; Gopalakrishnan, J.; Lazarov, R..
Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems.
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