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We consider the Stokes problem on a plane polygonal domain    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.

Partition of unity method on nonmatching grids for the Stokes problem