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Error Estimates for Nonconforming Finite Element Approximations of Drag and Lift in Channel Flows

by John, V., Tabata, M., Tobiska, L..

Series: 1998-03, Preprints

65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds
76D05 ~Navier-Stokes equations

We propose a new method for computing drag and lift acting
on bodies in channel flows by means of nonconforming finite
element approximations to the incompressible Navier--Stokes
equations. For the new formulas, a-priori error estimates
are given which cover both the standard nonconforming
finite element method and also stabilized discretizations
of upwind type to handle the case of higher Reynolds
numbers. For a two-dimensional DFG benchmark problem of a
laminar flow around a cylinder, numerical results of the
drag and the lift are presented. The numerical tests
confirm our theoretical results.

Navier-Stokes equations, drag and lift, nonconforming finie element methods