A comparative study of efficient iterative solvers for generalized Stokes equations

We consider a generalized Stokes equation with problem parameters 0 (size of the reaction term) and >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 . We give an overview of the main theoretical convergence results known for these methods. For a three-dimensional problem, discretized by the Hood–Taylor P2–P1 pair, we give results of numerical experiments. Copyright q 2007 John Wiley & Sons, Ltd.