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• W3137409987 abstract "A well-known strategy for building effective preconditioners for higher-order discretizations of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their low-order analogs. In this work, we show that high-quality preconditioners can also be derived for the Taylor-Hood discretization of the Stokes equations in much the same manner. In particular, we investigate the use of geometric multigrid based on the $boldsymbol{ mathbb{Q}}_1isoboldsymbol{ mathbb{Q}}_2/ mathbb{Q}_1$ discretization of the Stokes operator as a preconditioner for the $boldsymbol{ mathbb{Q}}_2/mathbb{Q}_1$ discretization of the Stokes system. We utilize local Fourier analysis to optimize the damping parameters for Vanka and Braess-Sarazin relaxation schemes and to achieve robust convergence. These results are then verified and compared against the measured multigrid performance. While geometric multigrid can be applied directly to the $boldsymbol{ mathbb{Q}}_2/mathbb{Q}_1$ system, our ultimate motivation is to apply algebraic multigrid within solvers for $boldsymbol{ mathbb{Q}}_2/mathbb{Q}_1$ systems via the $boldsymbol{ mathbb{Q}}_1isoboldsymbol{ mathbb{Q}}_2/ mathbb{Q}_1$ discretization, which will be considered in a companion paper." @default.
• W3137409987 created "2021-03-29" @default.
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• W3137409987 date "2021-03-22" @default.
• W3137409987 modified "2023-09-26" @default.
• W3137409987 title "Low-order preconditioning of the Stokes equations." @default.
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