PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Xiantao Li, Yuxi Zheng, Kris Jenssen, Jinchao Xu.

Abstract:
Title:	Canonical decompositions for Discontinuous Galerkin methods and Preconditioning
Seminar:	Computational and Applied Mathematics Colloquium
Speaker:	Blanca Ayuso de Dios, CRM, Barcelona Spain
We introduce a natural decomposition of the discontinuous Galerkin Finite Element spaces. For the lowest order case this decomposition is a direct sum of of the Crouzeix-Raviart non-conforming finite element space and a subspace that contains functions discontinuous at interior faces. Based on these decompositions we develop iterative and preconditioning techniques for the solution of the linear systems resulting from several discontinuous Galerkin (DG) Interior Penalty (IP) discretizations of elliptic problems. We analyze the convergence properties of these algorithms for both symmetric and non-symmetric IP schemes. We also present numerical examples confirming the theoretical results. Further extension to problems with jumps in the coefficients and linear elasticity will also be discussed. The talk is based on joint works with Ludmil T. Zikatanov from Penn State University (USA).