Numerical Analysis
Convergence of the Lagrange–Galerkin method for a fluid–rigid system
Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 59-64.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.04.007
San Martı́n, Jorge 1; Scheid, Jean-Francois 2; Takahashi, Takéo 2; Tucsnak, Marius 2

1 Departemento de Ingenierı́a Matemática, Universidad de Chile, Casilla 170/3-Correo 3, Santiago, Chile
2 Institut Elie Cartan, faculté des sciences, BP 239, 54506 Vandoeuvre-lès-Nancy cedex, France
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San Martı́n, Jorge; Scheid, Jean-Francois; Takahashi, Takéo; Tucsnak, Marius. 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. http://www.numdam.org/articles/10.1016/j.crma.2004.04.007/

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Cited by Sources:

INRIA Lorraine, Projet CORIDA.