Finite Element Approximation of the Nonstationary Navier–Stokes Problem III. Smoothing Property and Higher Order Error Estimates for Spatial Discretization

1988 ◽  
Vol 25 (3) ◽  
pp. 489-512 ◽  
Author(s):  
John G. Heywood ◽  
Rolf Rannacher
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Stokes Problem ◽  
Finite Element Approximation ◽  
Higher Order ◽  
Navier Stokes ◽  
Element Approximation ◽  
Spatial Discretization ◽  
Order Error ◽  
Smoothing Property

FINITE ELEMENT ERROR ANALYSIS OF SPACE AVERAGED FLOW FIELDS DEFINED BY A DIFFERENTIAL FILTER

2004 ◽  
Vol 14 (04) ◽  
pp. 603-618 ◽  
Author(s):  
ADRIAN DUNCA ◽  
VOLKER JOHN
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Flow Fields ◽  
Navier Stokes ◽  
Element Approximation ◽  
Navier Stokes Equations ◽  
Finite Element Approximations ◽  
Three Space ◽  
Element Error

This paper analyzes 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 [Formula: see text], the error of the filtered velocity [Formula: see text] and the filtered finite element approximation of the velocity [Formula: see text], converges under certain conditions of higher order than [Formula: see text], the error of the velocity and its finite element approximation. It is also proved that this statement stays true if the L2-error of finite element approximations of [Formula: see text] and [Formula: see text] is considered. Numerical tests in two and three space dimensions support the analytical results.

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