Domain Decomposition Preconditioning for Discontinuous Galerkin Approximation of Convection-Diffusion Problems

Code:
21/2008
Title:
Domain Decomposition Preconditioning for Discontinuous Galerkin Approximation of Convection-Diffusion Problems
Date:
Monday 29th September 2008
Author(s):
Antonietti, Paola; Suli, Endre
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Abstract:
We study a class of nonoverlapping Schwarz preconditioners for DG ap- proximations of convection-di usion equations. The generalized minimal residual (GMRES) Krylov space-based iterative solver is accelerated with the proposed preconditioners. We discuss the issue of convergence of the re- sulting preconditioned iterative method, and demonstrate through numer- ical computations that the classical Schwarz convergence theory for non- symmetric and indefinite problems developed by Cai and Widlund [SIAM J. Sci. Statist. Comput. 13 (1992) 243--258], [SIAM J. Numer. Anal. 30 (1993) 936--952] cannot be applied to explain theoretically the converge observed numerically