|Title:|| Domain Decomposition Preconditioning for Discontinuous Galerkin Approximation of Convection-Diffusion Problems|
|Date:|| Monday 29th September 2008|
|Author(s) :|| Antonietti, Paola; Suli, Endre|
|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|