Approximating local averages of fluid velocities: The Stokes problem

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