The finite element immersed boundary method: model, stability, and numerical results

The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems. Recently, a finite element version of the IBM as been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. In this paper we shall review our model and present numerical results in two and three dimensions fully confirming the good performance of our scheme. A preliminary stability analysis shows a condition linking the time step size and the discretization parameter along the immersed boundary. This condition is confirmed by our numerical experiments.