Overlapping Schwarz methods for mixed linear elasticity and Stokes problems

Overlapping Schwarz preconditioners are introduced and studied for saddle p oint problems with a penalty term, such as Stokes equations and mixed formu lations of linear elasticity. These preconditioners are based on the soluti on of local saddle point problems on overlapping subdomains and the solutio n of a coarse saddle point problem. Numerical experiments show that these a re parallel and scalable preconditioners, since the rate of convergence of the preconditioned operator is independent of the mesh size h, the number o f subdomains N, and the penalty parameter. (C) 1998 Elsevier Science S.A. A ll rights reserved.