A class of block smoothers for multigrid solution of saddle point problems with application to fluid flow

We design and analyse an iterative method, which uses a specific block smoother for the multigrid cycle. Among many possibilities we choose a few multigrid iterations as the smoother's blocks. The result is a multilevel procedure that works for regular saddle point problems and features all good properties of the classical multigrid for elliptic problems, such as the optimal complexity and convergence rate independent of the number of levels.