Convergence analysis of a projection semi-implicit coupling scheme for fluid-structure interaction problems.

International audienceIn this paper, we provide a convergence analysis of a projection semi- implicit scheme for the simulation of fluid-structure systems involving an incom- pressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semi-implicit time-stepping strategy are respectively used for space and time discretization. The fluid is described by the Stokes equations, the structure by the classical linear elastodynamics equations (linearized elasticity, plate or shell models) and all changes of geometry are neglected. We derive an error estimate in finite time and we prove that the time discretization error of the coupling scheme is of order 1/2. Finally, some numerical experiments that confirm the theoretical analysis are presented