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Partition of unity method on nonmatching grids for the Stokes problem. (English) Zbl 1148.76305
Summary: We consider the Stokes problem on a plane polygonal domain \(\Omega \subset \mathbb R^2\). We propose a finite element method for overlapping or nonmatching grids for the Stokes problem based on the partition of unity method. We prove that the discrete inf-sup condition holds with a constant independent of the overlapping size of the subdomains. The results are valid for multiple subdomains and any spatial dimension.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
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
76M10 Finite element methods applied to problems in fluid mechanics
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