  The main goal of the paper is to show new stability and localization results
for the finite element solution of the Stokes system in $W^{1,\infty}$ and
$L^{\infty}$ norms under standard assumptions on the finite element spaces on
quasi-uniform meshes in two and three dimensions. Although interior error
estimates are well-developed for the elliptic problem, they appear to be new
for the Stokes system on unstructured meshes. To obtain these results we extend
previously known stability estimates for the Stokes system using regularized
Green's functions.
