Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra

Abstract

The aim of the paper is to show the stability of the finite element solution for the Stokes system in W ∞ 1 W^1_\infty norm on general convex polyhedral domain. In contrast to previously known results, W r 2 W^2_r regularity for r > 3 r>3 , which does not hold for general convex polyhedral domains, is not required. The argument uses recently available sharp Hölder pointwise estimates of the corresponding Green’s matrix together with novel local energy error estimates, which do not involve an error of the pressure in a weaker norm.