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A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions

Published online by Cambridge University Press:  21 August 2009

Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr
Frédéric Hecht
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr
Rüdiger Verfürth
Affiliation:
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. ruediger.verfuerth@ruhr-uni-bochum.de
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Abstract

We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish a priori and a posteriori error estimates.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

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