We consider the widely used continuous $\mathcal{Q}_{k}$-$\mathcal{Q}_{k-1}$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Sch\"oberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.
翻译：我们认为,在两个和三个空间层面将斯托克斯和通用斯托克斯系统的有限元素分解成两个和通用斯托克斯系统的四边或六面制泰勒-Hood元素中,广泛使用的连续美元(mathcal ⁇ k}$-mathcal ⁇ k-1}$-mathcal ⁇ k}$(mathcal ⁇ k}-1}$)四边或六面制泰勒-Hood元素。为了快速解决相应的对称但无限期的有限元素方程式系统,我们提议并分析基于适当缩放的切比谢夫-贾科比平滑剂的无矩阵单方形几格数多格解器。这项分析基于Sch\'oberl和Zulehner(2003年)的结果。我们提出并讨论典型基准问题的若干数字结果。
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