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

Volker John
Lutz Tobiska
Otto-von-Guericke-Universität Magdeburg, Germany

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 L2-projection as well as simple averaging are considered as prolongation. The W-cycle convergence in the L2-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.