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ABSTRACT:
The constrained relaxation 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 developed and 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.