  In this paper, we present a novel local and parallel two-grid finite element
scheme for solving the Stokes equations, and rigorously establish its a priori
error estimates. The scheme admits simultaneously small scales of subproblems
and distances between subdomains and its expansions, and hence can be
expandable. Based on the a priori error estimates, we provide a corresponding
iterative scheme with suitable iteration number. The resulting iterative scheme
can 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 $H$ and
the fine mesh size $h$ are properly chosen. Finally, some numerical tests
including 2-D and 3-D cases are carried out to verify our theoretical results.
