Local and parallel finite element post-processing scheme for the Stokes problem

A local and parallel finite element post-processing scheme based on partition of unity method is proposed and analyzed in this paper for the Stokes problem. Firstly, a standard Galerkin finite element method on a relatively coarse grid is used to obtain the approximation of the lower frequency components. Secondly, the higher frequency components are computed on fine grids by some local and parallel procedure to post-process the standard Galerkin approximation. The motivation of the proposed local and parallel finite element post-processing scheme is based on the superposition principle. Finally, to eliminate the effect of the Dirichlet boundary conditions which are imposed on the internal artificial boundaries, a global coarse grid correction is done to improve the L2-accuracy of the approximation.