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

by V.John, L. Tobiska.

Series: 1999-03, Preprints

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

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.

nonconforming finite element discretizations, coupled multigrid methods,

This paper was published in:
Computing 64,