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Multigrid methods for the generalized Stokes equations based on mixed finite element methods. (English) Zbl 0998.65123

Multigrid methods for the generalized Stokes equations discretized by mixed finite element methods are developed. The multigrid algorithm with the criterion for prolongation operators and the convergence analysis are established. It is shown that the multigrid algorithm converges optimally if the prolongation satisfies the criterion. For nonconforming elements, it is shown that the usual local averaging technique can be replaced by a computationally cheaper alternative.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
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