99-03

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

by V.John; L. Tobiska

 

Preprint series: 99-03, Preprints

The paper is published: Computing 64, 307 - 321, 2000, with the title \'A Coupled Multigrid Method for Nonconforming Finite Element Discretizations of the 2D--Stokes Equation\'

MSC:
65N12 Stability and convergence of numerical methods
65N22 Solution of discretized equations, See also {65Fxx, 65Hxx}
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,


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