Fast iterative solvers for discrete Stokes equations

Abstract. We consider saddle point problems that result from the ¯nite element discretization of stationary and instationary Stokes equations. Three e±cient iterative solvers for these problems are treated, namely the preconditioned CG method introduced by Bramble and Pasciak, the pre-conditioned MINRES method and a method due to Bank et al. We give a detailed overview of algorithmic aspects and theoretical convergence results. For the method of Bank et al a new con-vergence analysis is presented. A comparative study of the three methods for a 3D Stokes problem discretized by the Hood-Taylor P2 ¡ P1 ¯nite element pair is given. AMS subject classi¯cations. 65N30, 65F1