A comparative study of efficient iterative solvers for generalized Stokes equations

We consider a generalized Stokes equation with problem parameters xi >= 0 (size of the reaction term) and nu>0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess-Sarazin and Vanka-type smoothers, a preconditioned MINRES method and an inexact Uzawa method. We present a comparative study of these methods. An important issue is the dependence of the rate of convergence of these methods on the mesh size parameter and on the problem parameters and v. We give an overview of the main theoretical convergence results known for these methods. For a three-dimensional problem, discretized by the Hood-Taylor P-2-P-1 pair, we give results of numerical experiments. Copyright (C) 2007 John Wiley & Sons, Ltd.