A two-level additive Schwarz preconditioner for the stationary Stokes equations

We consider the stationary Stokes equations on a polygonal domain whose boundary has more than one component, i.e., flow with obstacles. A two-level additive Schwarz preconditioner is developed for the divergence-free nonconforming P1 finite element. The condition number of the preconditioned system is shown to be bounded independent of mesh sizes and the number of subdomains in the case of generous overlap.This work was supported in part by the National Science Foundation under Grant Nos. DMS-92-09332 and DMS-94-96275.