A coupled multigrid method for nonconforming finite element discretizations of the 2D-Stokes equation

This paper investigates a multigrid method for the solution of the saddle p oint formulation of the discrete Stokes equation obtained with inf-sup stab le nonconforming finite elements of lowest order. A smoother proposed by Br aess and Sarazin (1997) is used and L-2-projection as well as simple averag ing 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 decrea sing with increasing number of smoothing steps is proven. Numerical tests c onfirm the theoretically predicted results.