Making DG methods competitive with mixed methods

Jay Gopalakrishnan

Email: jayg@ufl.edu
Postal address: 358 Little Hall, University of Florida, Gainesville, FL 32611-8105

While domain decomposition techniques are well known to yield good iterative solvers, in this talk we will apply some domain decomposition ideas to obtain new discretization techniques.  When certain domain decomposition concepts are applied with elements as subdomains, we obtain hybridized finite element methods.

While the advantages of hybridized mixed methods have long been known, it was not clear if such techniques could be developed for discontinuous Galerkin (DG) methods. In this talk, we will develop a family of hybridized DG methods. Among the existing DG methods, we will highlight one due to Ewing, Wang, and Yang, as the only interior penalty type method that we are able to hybridize.  The importance of hybridized DG methods lies in the fact such DG methods give systems with size and sparsity identical to mixed methods. Thus, the often made criticism that DG methods have too many unknowns do not apply to hybridized DG methods.