Convergence of the Lagrange-Galerkin method for the Equations Modelling the Motion of a Fluid-Rigid System

Jorge San Martin (1) , Jean-François Scheid (2, 3) , Takéo Takahashi (2, 3) , Marius Tucsnak (2, 3)

1 DIM - Departamento de Ingeniería Matemática [Santiago]
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECN - Institut Élie Cartan de Nancy

In this paper, we consider a Lagrange-Galerkin scheme to approximate a two dimensional fluid-rigid body problem. The equations of the system are the 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.

Mots clés: fluid-structure interaction; incompressible Navier-Stokes equations; finite element method; Lagrange-Galerkin method

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jorge San Martin, Jean-François Scheid, Takéo Takahashi, Marius Tucsnak. Convergence of the Lagrange-Galerkin method for the Equations Modelling the Motion of a Fluid-Rigid System. SIAM Journal on Numerical Analysis, 2005, Volume 43, Issue 4, pp.1536-1571. ⟨10.1137/S0036142903438161⟩. ⟨hal-00092094⟩