Volume 43, Number 6, November-December 2009
|Page(s)||1185 - 1201|
|Published online||21 August 2009|
A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. firstname.lastname@example.org; email@example.com
2 Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. firstname.lastname@example.org
Revised: 25 May 2009
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.
Mathematics Subject Classification: 65N30 / 65N15 / 65J15
Key words: Three-dimensional Navier–Stokes equations / mixed boundary conditions / finite element methods / a priori error estimates / a posteriori error estimates.
© EDP Sciences, SMAI, 2009
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