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

05/31/2022

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by   Daniel Jodlbauer, et al.

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We consider the widely used continuous 𝒬_k-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 Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.