272 RWTH Publication No: 47226        2007        IGPM272.pdf
TITLE A Comparative Study of Efficient Iterative Solvers for Generalized Stokes Equations
AUTHORS Maxim Larin, Arnold Reusken
ABSTRACT 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 c 2006 John Wiley & Sons, Ltd.
KEYWORDS generalized Stokes problem, preconditioned MINRES, inexact Uzawa method, multigrid methods, Vanka and Braess-Sarazin smoothers
DOI 10.1002/nla.561
PUBLICATION Numerical linear algebra with applications
15(1), 13-34 (2008)