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.
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.
Accepted:
Published online:
Jorge San Martı́n 1; Jean-Francois Scheid 2; Takéo Takahashi 2; Marius Tucsnak 2
@article{CRMATH_2004__339_1_59_0,
author = {Jorge San Mart{\i}́n and Jean-Francois Scheid and Tak\'eo Takahashi and Marius Tucsnak},
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},
}
TY - JOUR AU - Jorge San Martı́n AU - Jean-Francois Scheid AU - Takéo Takahashi AU - Marius Tucsnak 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 DO - 10.1016/j.crma.2004.04.007 LA - en ID - CRMATH_2004__339_1_59_0 ER -
%0 Journal Article %A Jorge San Martı́n %A Jean-Francois Scheid %A Takéo Takahashi %A Marius Tucsnak %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 %R 10.1016/j.crma.2004.04.007 %G en %F CRMATH_2004__339_1_59_0
Jorge San Martı́n; Jean-Francois Scheid; Takéo Takahashi; Marius Tucsnak. Convergence of the Lagrange–Galerkin method for a fluid–rigid system. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 59-64. doi : 10.1016/j.crma.2004.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.007/
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☆ INRIA Lorraine, Projet CORIDA.
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