| Issue |
ESAIM: M2AN
Volume 43, Number 6, November-December 2009
|
|
|---|---|---|
| Page(s) | 1185 - 1201 | |
| DOI | https://doi.org/10.1051/m2an/2009035 | |
| Published online | 21 August 2009 | |
A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions
1
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
2
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. ruediger.verfuerth@ruhr-uni-bochum.de
Received:
1
December
2008
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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