Numerische Mathematik

, Volume 115, Issue 2, pp 261–287 | Cite as

Error estimate of the P1 nonconforming finite element method for the penalized unsteady Navier-Stokes equations

Article

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 P1 nonconforming finite element space for the spatial discretization. Optimal \({\epsilon}\)-uniform error estimations for both velocity and pressure are obtained.

Mathematics Subject Classification (2000)

65N30 76D05 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  2. 2.Division of MathematicsUniversity of DundeeDundeeScotland, UK

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