Fast Iterative Solvers for Discrete Stokes Equations

We consider saddle point problems that result from the finite element discretization of stationary and nonstationary Stokes equations. Three efficient iterative solvers for these problems are treated, namely, the preconditioned conjugate gradient method introduced by Bramble and Pasciak, the preconditioned 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 convergence analysis is presented. A comparative study of the three methods for a three-dimensional Stokes problem discretized by the Hood--Taylor P2 -P1 finite element pair is given.