Approximating Local Averages of Fluid Velocities: The Stokes Problem

Abstract

As a first step to developing mathematical support for finite element approximation to the large eddies in fluid motion we consider herein the Stokes problem. We show that the local average of the usual approximate flow field u ^h over radius δ provides a very accurate approximation to the flow structures of O(δ) or greater. The extra accuracy appears for quadratic or higher velocity elements and degrades to the usual finite element accuracy as the averaging radius δ→h (the local meshwidth). We give both a priori and a posteriori error estimates incorporating this effect.