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1999-03

A Coupled Multigrid Method for Nonconforming Finite Element Discretizations of the Stokes Equation

by V.John, L. Tobiska.


Series: 1999-03, Preprints

MSC:
65N12 Stability and convergence of numerical methods
65N22 Solution of discretized equations
65N55 Multigrid methods; domain decomposition

Abstract:
This paper investigates a multigrid method for the solution of the
saddle point formulation of the discrete Stokes equation obtained with
inf--sup stable nonconforming finite elements of lowest order. A
smoother proposed by Braess and Sarazin (1997) is used and
$L^2$--projection as well as simple averaging are considered as
prolongation. The W--cycle convergence in the $L^2$--norm of
the velocity with a rate independently of
the level and linearly decreasing with increasing number of smoothing
steps is proven. Numerical tests confirm the theoretically predicted results.

Keywords:
nonconforming finite element discretizations, coupled multigrid methods,

This paper was published in:
Computing 64,