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.
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Received January 19, 1999; revised September 13, 1999
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John, V., Tobiska, L. A Coupled Multigrid Method for Nonconforming Finite Element Discretizations of the 2D-Stokes Equation. Computing 64, 307–321 (2000). https://doi.org/10.1007/s006070070027
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DOI: https://doi.org/10.1007/s006070070027