Preconditioning Interior Penalty Discontinuous Galerkin Methods

Wednesday, December 1, 2010 - 9:45am - 10:30am
Keller 3-180
Blanca Ayuso de Dios (Centre de Recerca Matemàtica )
We propose iterative methods for the solution of the linear systems resulting from

Interior Penalty (IP)  discontinuous Galerkin (DG)  approximations of elliptic problems.

The precoonditioners are derived from a natural decomposition of the DG finite element spaces. We present the convergence analysis of the solvers for both symmetric and non-symmetric IP schemes. Extension to problems with jumps in the coefficients and linear elasticity will also be discussed. We describe in detail the preconditioning techniques for low order (piece-wise linear ) IP methods and we indicate how to proceed in the case of high order (odd degree) approximations. The talk is based on joint works with Ludmil T. Zikatanov from  Penn State University (USA).