Numerical analysis of some decoupling techniques for the approximation of the unsteady fluid structure interaction

This paper deals with the numerical analysis of some algorithms for the simulation of the interaction between a fluid and a structure in the case where the deformation of the structure induces an evolution in the fluid domain. This is a highly nonlinear problem and the algorithms of time decoupling are very numerous and not completely well understood. We study three of them for a one-dimensional representative problem. We prove that the considered algorithms are stable and we also prove that one of them is convergent.