Zurück zu den Preprints des Jahres 2003


Finite element error analysis of space averaged flow fields defined by a differential filter

by Dunca, A., John, V..

Series: 2003-13, Preprints

65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
76D05 ~Navier-Stokes equations

This paper analyses finite element approximations of space averaged
flow fields which are given by filtering, i.e. averaging in space, the
solution of the steady state Stokes and Navier-Stokes equations with a
differential filter. It is shown that $\|\overline{\bu}
-\overline{\bu^h}\|_{L^2}$, the error of the filtered velocity $\overline{\bu}$ and the
filtered finite element approximation of the velocity
$\overline{\bu^h}$, converges under certain conditions of higher order
than $\|{\bu}
-{\bu^h}\|_{L^2}$, the error of the velocity and its finite element
approximation. It is also proved that this statement stays true if the
$L^2$-error of finite element approximations of $\overline{\bu}$ and
$\overline{\bu^h}$ is considered. Numerical tests in two and three
space dimensions support the analytical results.

differential filter, convergence of finite element method