Overlapping Schwarz methods for mixed linear elasticity and Stokes problems Original Research Article

Overlapping Schwarz preconditioners are introduced and studied for saddle point problems with a penalty term, such as Stokes equations and mixed formulations of linear elasticity. These preconditioners are based on the solution of local saddle point problems on overlapping subdomains and the solution of a coarse saddle point problem. Numerical experiments show that these are parallel and scalable preconditioners, since the rate of convergence of the preconditioned operator is independent of the mesh size h, the number of subdomains N, and the penalty parameter.