MULTIGRID AND KRYLOV SUBSPACE METHODS FOR THE DISCRETE STOKES EQUATIONS

                               Howard C. Elman
                      Department of Computer Science and
                   Institute for Advanced Computer Studies
                            University of Maryland
                            College Park, MD 20742
                               elman@cs.umd.edu

Abstract.  Discretization of the Stokes equations produces a symmetric
indefinite system of linear equations.  For stable discretizations, a variety
of numerical methods have been proposed that have rates of convergence
independent of the mesh size used in the discretization.  In this paper, we
compare the performance of four such methods:  variants of the Uzawa,
preconditioned conjugate gradient, preconditioned conjugate residual, and
multigrid methods, for solving several two-dimensional model problems.  The
results indicate that where it is applicable, multigrid with smoothing based
on incomplete factorizaton is more efficient than the other methods, but
typically by no more than a factor of two.  The conjugate residual method has
the advantages of being both independent of iteration parameters and widely
applicable.