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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.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria

    Xiliang Lu

  2. Division of Mathematics, University of Dundee, 23 Perth Road, Dundee, DD1 4HN, Scotland, UK

    Ping Lin

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  1. Xiliang Lu
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Correspondence to Xiliang Lu.

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Lu, X., Lin, P. Error estimate of the P 1 nonconforming finite element method for the penalized unsteady Navier-Stokes equations. Numer. Math. 115, 261–287 (2010). https://doi.org/10.1007/s00211-009-0277-8

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  • DOI: https://doi.org/10.1007/s00211-009-0277-8

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