Discrete models for fluid-structure interactions: the Finite Element   Immersed Boundary Method
  The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present the different formulation proposed in our research and highlight the advantages of the one based on a distributed Lagrange multiplier (DLM-IBM) over the original FE-IBM. 
Daniele Boffi, Lucia Gastaldi
math.NA