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Zbl 1145.65097
He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian
Local and parallel finite element algorithms for the Stokes problem. (English)
[J] Numer. Math. 109, No. 3, 415-434 (2008). ISSN 0029-599X; ISSN 0945-3245/e

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.
[Dietrich Braess (Bochum)]

MSC 2000:: *65N30 Finite numerical 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 flows
76M10 Finite element methods
65N50 Mesh generation and refinement (BVP of PDE)
65Y05 Parallel computation (numerical methods)

Keywords: Stokes problem; local estimates; parallel algorithms; finite element; multigrid algorithms; local refinements

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