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We consider the widely used continuous $\mathcal{Q}_{k}$-$\mathcal{Q}_{k-1}$quadrilateral or hexahedral Taylor-Hood elements for the finite elementdiscretization of the Stokes and generalized Stokes systems in two and threespatial dimensions. For the fast solution of the corresponding symmetric, butindefinite system of finite element equations, we propose and analyzematrix-free monolithic geometric multigrid solvers that are based onappropriately scaled Chebyshev-Jacobi smoothers. The analysis is based onresults by Sch\"oberl and Zulehner (2003). We present and discuss severalnumerical results for typical benchmark problems.

Matrix-free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems