the Institute for Theoretical and Engineering Science
Department of Mathematics

University of Houston

Scientific Computing Seminar

Professor Raytcho Lazarov
Department of Mathematics
Texas A&M University

Hybridization of FE Approximations of Elliptic Problems
with Application to Discontinuous Galerkin Methods$^*$
$^*$joint work with B. Cockburn (U. Minnesota), J. Gopalakrishnan (U. Florida)

Thursday, March 1, 2007
3:00 PM- 4:00 PM
Room 634 S&R1

Abstract: We shall present a general hybridization technique for finite element approximations of self-adjoint second order elliptic equations. This new framework combines the main ideas of hybridized mixed finite element method with the technique of lifting operators from discontinuous Galerkin (DG) approximations. As a result, we get a unified hybridization technique that can be applied for DG, locally DG, mixed, nonconforming, and conforming finite element approximations of second order problems.

In the talk we shall introduce the hybridization framework and present its main ingredients: (1) local solvers and their finite element spaces, (2) the numerical traces of the solution and the flux, (3) the space of the Lagrange multiplier.

We show that this framework reproduces the known hybridization of the standard mixed finite element method. Specialized to the interior penalty (IP) DG approximations the proposed hybridization method fully characterizes the class of hybridizable IP DG schemes. We show that from the known IP DG methods only a scheme due to Ewing, Wang, and Yang is hybridizable.

This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.