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A comparative study of efficient iterative solvers for generalized Stokes equations

We consider a generalized Stokes equation with problem parameters ξ⩾0 (size of the reaction term) and ν>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 ξ and ν. 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 © 2007 John Wiley & Sons, Ltd.