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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 $D\subset \subset {{\Omega }}_{0}\subset {\Omega }$. The approximation properties in $D$ depend less on the meshsize in ${\Omega }\setminus {{\Omega }}_{0}$ than on the meshsize in ${{\Omega }}_{0}$. This is helpful in the analyisis of local refinements or parallel iterations on subdomains.
##### MSC:
 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65N15 Error bounds (BVP of PDE) 65N55 Multigrid methods; domain decomposition (BVP of PDE) 35Q30 Stokes and Navier-Stokes equations 76D07 Stokes and related (Oseen, etc.) flows 76M10 Finite element methods (fluid mechanics) 65N50 Mesh generation and refinement (BVP of PDE) 65Y05 Parallel computation (numerical methods)