Convergence of the Lagrange-Galerkin method for the equations modelling the motion of a fluid-rigid system

Abstract

In this paper, we consider a Lagrange-Galerkin scheme to approximate a two dimensional °uid-rigid body problem. The equations of the system are the Navier- Stokes equations in the °uid part, coupled with ordinary di®erential equations for the dynamics of the rigid body. In this problem, the equations of the °uid 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 ¯nite elements with a ¯xed mesh. Our main result asserts the convergence of this scheme.