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

Christine Bernardi; Frédéric Hecht; Rüdiger Verfürth

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 6, page 1185-1201
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bernardi, Christine, Hecht, Frédéric, and Verfürth, Rüdiger. "A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis 43.6 (2009): 1185-1201. <http://eudml.org/doc/250614>.

@article{Bernardi2009,
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. },
author = {Bernardi, Christine, Hecht, Frédéric, Verfürth, Rüdiger},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Three-dimensional Navier–Stokes equations; mixed boundary conditions; finite element methods; a priori error estimates; a posteriori error estimates.; three-dimensional Navier-Stokes equations; a priori error estimates; a posteriori error estimates},
language = {eng},
month = {8},
number = {6},
pages = {1185-1201},
publisher = {EDP Sciences},
title = {A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions},
url = {http://eudml.org/doc/250614},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Bernardi, Christine
AU - Hecht, Frédéric
AU - Verfürth, Rüdiger
TI - A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/8//
PB - EDP Sciences
VL - 43
IS - 6
SP - 1185
EP - 1201
AB - 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.
LA - eng
KW - Three-dimensional Navier–Stokes equations; mixed boundary conditions; finite element methods; a priori error estimates; a posteriori error estimates.; three-dimensional Navier-Stokes equations; a priori error estimates; a posteriori error estimates
UR - http://eudml.org/doc/250614
ER -

References

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