Multigrid Methods for the Stokes Equations using Distributive Gauss-Seidel Relaxations based on the Least Squares Commutator

A distributive Gauss–Seidel relaxation based on the least squares commutator is devised for the saddle-point systems arising from the discretized Stokes equations. Based on that, an efficient multigrid method is developed for finite element discretizations of the Stokes equations on both structured grids and unstructured grids. On rectangular grids, an auxiliary spacemultigridmethod using onemultigrid cycle for theMarker andCell scheme as auxiliary space correction and least squares commutator distributive Gauss–Seidel relaxation as a smoother is shown to be very efficient and outperforms the popular block preconditioned Krylov subspace methods.