Stability Results for the Finite Element Approach to the Immersed Boundary Method

The immersed boundary method in its original formulation, introduced by Peskin in [9], exhibits a high degree of numerical stiffness. A finite element approach was proposed by Boffi et al. [1] and further developed in Boffi et al. [2,3] to solve some of the difficulties arising from the original formulation. We present a stability analysis for the two dimensional case with some numerical tests which show how to choose the numerical parameters in order to obtain optimal stability