Convergence of a finite element discretization for an Arbitrary Lagrangian Eulerian formulation of a fluid-structure interaction problem

Guillaume Legendre (1) , Takéo Takahashi (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications

In this paper, we propose a numerical scheme to compute the motion of a two-dimensional rigid body in a viscous fluid, modeled by the Navier-Stokes equations. Our method combines a finite element approximations and the use of the method of characteristics to solve an Arbitrary Lagrangian Eulerian formulation of the problem. We derive error estimates for this scheme which imply its convergence.

Domaines: Equations aux dérivées partielles [math.AP]

Guillaume Legendre, Takéo Takahashi. Convergence of a finite element discretization for an Arbitrary Lagrangian Eulerian formulation of a fluid-structure interaction problem. 2007. ⟨hal-00142870v1⟩