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

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


Preprint series: 98-03, Preprints

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds
76D05 Navier-Stokes equations, See also {35Q30}


Abstract: 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.

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

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