Local and parallel finite element algorithms for the Stokes problem. (English) Zbl 1145.65097

He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian

Numer. Math. 109, No. 3, 415-434 (2008).

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.

Reviewer: Dietrich Braess (Bochum)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
35Q30	Navier-Stokes equations
76D07	Stokes and related (Oseen, etc.) flows
76M10	Finite element methods applied to problems in fluid mechanics
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65Y05	Parallel numerical computation

Keywords:

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

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