, Volume 115, Issue 2, pp 261-287
Date: 02 Dec 2009

Error estimate of the P 1 nonconforming finite element method for the penalized unsteady Navier-Stokes equations

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Abstract

We consider a finite element method for the penalty formulation of the time dependent Navier-Stokes equations. Usually the improper choice of the finite element space will lead that the error estimate (inversely) depends on the penalty parameter \({\epsilon}\) . We use the classical P 1 nonconforming finite element space for the spatial discretization. Optimal \({\epsilon}\) -uniform error estimations for both velocity and pressure are obtained.