Convergence of the Lagrange–Galerkin method for a fluid–rigid system

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. To cite this article: J. San Martin et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).