[Convergence de la méthode de Lagrange–Galerkin pour un système fluide–rigide]
Dans cette Note, nous considérons un schéma de Lagrange–Galerkin pour approcher un problème fluide–rigide. Le système est modélisé par les équations de Navier–Stokes incompressible, pour la partie fluide, couplées avec des équations différentielles ordinaires pour la dynamique du corps rigide. Dans ce problème, les équations du fluide sont écrites sur un domaine dont la variation est une des inconnues. Nous introduisons une méthode numérique basée sur l'utilisation des caractéristiques et des éléments finis associés à un maillage fixe. Notre résultat principal est la convergence de ce schéma.
In this Note, we consider a Lagrange–Galerkin scheme to approximate a two dimensional fluid–rigid body problem. The system is modelled by the incompressible Navier–Stokes equations in the fluid part, coupled with ordinary differential equations for the dynamics of the rigid body. In this problem, the equations of the fluid are written in a domain whose variation is one of the unknowns. We introduce a numerical method based on the use of characteristics and on finite elements with a fixed mesh. Our main result asserts the convergence of this scheme.
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@article{CRMATH_2004__339_1_59_0,
author = {San Mart{\i}́n, Jorge and Scheid, Jean-Francois and Takahashi, Tak\'eo and Tucsnak, Marius},
title = {Convergence of the {Lagrange{\textendash}Galerkin} method for a fluid{\textendash}rigid system},
journal = {Comptes Rendus. Math\'ematique},
pages = {59--64},
publisher = {Elsevier},
volume = {339},
number = {1},
year = {2004},
doi = {10.1016/j.crma.2004.04.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.04.007/}
}
TY - JOUR AU - San Martı́n, Jorge AU - Scheid, Jean-Francois AU - Takahashi, Takéo AU - Tucsnak, Marius TI - Convergence of the Lagrange–Galerkin method for a fluid–rigid system JO - Comptes Rendus. Mathématique PY - 2004 SP - 59 EP - 64 VL - 339 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.04.007/ DO - 10.1016/j.crma.2004.04.007 LA - en ID - CRMATH_2004__339_1_59_0 ER -
%0 Journal Article %A San Martı́n, Jorge %A Scheid, Jean-Francois %A Takahashi, Takéo %A Tucsnak, Marius %T Convergence of the Lagrange–Galerkin method for a fluid–rigid system %J Comptes Rendus. Mathématique %D 2004 %P 59-64 %V 339 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.04.007/ %R 10.1016/j.crma.2004.04.007 %G en %F CRMATH_2004__339_1_59_0
San Martı́n, Jorge; Scheid, Jean-Francois; Takahashi, Takéo; Tucsnak, Marius. Convergence of the Lagrange–Galerkin method for a fluid–rigid system. Comptes Rendus. Mathématique, Tome 339 (2004) no. 1, pp. 59-64. doi : 10.1016/j.crma.2004.04.007. http://www.numdam.org/articles/10.1016/j.crma.2004.04.007/
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