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Local and parallel finite element algorithms for the Stokes problem. (English) Zbl 1145.65097
Some local and parallel finite element algorithms for the Stokes problem are proposed and analyzed. In addition to the well-known ideas of multigrid algorithms, local properties of finite element solutions are used that are known from the study of pollution effects. Let DΩ 0 Ω. The approximation properties in D depend less on the meshsize in ΩΩ 0 than on the meshsize in Ω 0 . This is helpful in the analyisis of local refinements or parallel iterations on subdomains.
MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
35Q30Stokes and Navier-Stokes equations
76D07Stokes and related (Oseen, etc.) flows
76M10Finite element methods (fluid mechanics)
65N50Mesh generation and refinement (BVP of PDE)
65Y05Parallel computation (numerical methods)
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