Stability Analysis of Finite Element Method for Stokes Problem on Overlapping Non-Matching Grids

In this paper, the steady-state Stokes problem is discussed on a plane polygonal domain . We propose a finite element method on overlapping non-matching grids for the Stokes problem based on the partition of unity method. The construction and stability analysis of a global conforming finite element method are studied, and our results are valid for any spatial dimensions.