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Stabilized finite element method for Navier-Stokes equations with physical boundary conditions


Authors: M. Amara, D. Capatina-Papaghiuc and D. Trujillo
Journal: Math. Comp. 76 (2007), 1195-1217
MSC (2000): Primary 35Q30, 65N12; Secondary 65N30
DOI: https://doi.org/10.1090/S0025-5718-07-01929-1
Published electronically: March 15, 2007
MathSciNet review: 2299771
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Abstract: This paper deals with the numerical approximation of the 2D and 3D Navier-Stokes equations, satisfying nonstandard boundary conditions. This lays on the finite element discretisation of the corresponding Stokes problem, which is achieved through a three-fields stabilized mixed formulation. A priori and a posteriori error bounds are established for the nonlinear problem, ascertaining the convergence of the method. Finally, numerical tests are presented, including mesh refinement via error indicators.


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Additional Information

M. Amara
Affiliation: Laboratoire de Mathématiques Appliquées-CNRS UMR5142, Université de Pau et des Pays de l’Adour, BP 1155, 64013 PAU CEDEX
Email: mohamed.amara@univ-pau.fr

D. Capatina-Papaghiuc
Affiliation: Laboratoire de Mathématiques Appliquées-CNRS UMR5142, Université de Pau et des Pays de l’Adour, BP 1155, 64013 PAU CEDEX
Email: daniela.capatina@univ-pau.dr

D. Trujillo
Affiliation: Laboratoire de Mathématiques Appliquées-CNRS UMR5142, Université de Pau et des Pays de l’Adour, BP 1155, 64013 PAU CEDEX
Email: david.trujillo@univ-pau.fr

DOI: https://doi.org/10.1090/S0025-5718-07-01929-1
Received by editor(s): June 4, 2004
Received by editor(s) in revised form: July 6, 2005
Published electronically: March 15, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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