Multigrid methods for saddle point systems using constrained smoothers

The constrained smoother for solving the saddle point system arising from the constrained minimization problem is a relaxation scheme such that the iteration remains in the constrained subspace. A multigrid method using constrained smoothers for saddle point systems is analyzed in this paper. Uniform convergence of two‐level and W‐cycle multigrid methods, with sufficient many smoothing steps and full regularity assumptions, are obtained for some stable finite element discretization of Stokes equations. For Braess–Sarazin smoother, a convergence theory using only partial regularity assumption is also developed.