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In this paper, we present a novel local and parallel two-grid finite elementscheme for solving the Stokes equations, and rigorously establish its a priorierror estimates. The scheme admits simultaneously small scales of subproblemsand distances between subdomains and its expansions, and hence can beexpandable. Based on the a priori error estimates, we provide a correspondingiterative scheme with suitable iteration number. The resulting iterative schemecan reach the optimal convergence orders within specific two-grid iterations($O(|\ln H|^2)$ in 2-D and $O(|\ln H|)$ in 3-D) if the coarse mesh size $H$ andthe fine mesh size $h$ are properly chosen. Finally, some numerical testsincluding 2-D and 3-D cases are carried out to verify our theoretical results.

Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations