Published

Multi-Grid Methods for Saddle Point Systems using Constrained Smoothers

Long Chen

Computers and Mathematics with Applications, 70(12) 2854-2866, 2015.

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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.