  A multigrid method for the Stokes system discretized with an Hdiv-conforming
discontinuous Galerkin method is presented. It acts on the combined velocity
and pressure spaces and thus does not need a Schur complement approximation.
The smoothers used are of overlapping Schwarz type and employ a local Helmholtz
decomposition. Additionally, we use the fact that the discretization provides
nested divergence free subspaces. We present the convergence analysis and
numerical evidence that convergence rates are not only independent of mesh
size, but also reasonably small.
