  In the present paper we propose a coupled multigrid method for generalized
Stokes flow problems. Such problems occur as subproblems in implicit
time-stepping approaches for time-dependent Stokes problems. The discretized
Stokes system is a large-scale linear system whose condition number depends on
the grid size of the spatial discretization and of the length of the time step.
Recently, for this problem a coupled multigrid method has been proposed, where
in each smoothing step a Poisson problem has to be solved (approximately) for
the pressure field.
  In the present paper, we propose a coupled multigrid method where the
solution of such sub-problems is not needed. We prove that the proposed method
shows robust convergence behavior in the grid size of the spatial
discretization and of the length of the time-step.
