Geodesic
The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 711-724.

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The Immersed Boundary Method (IBM) has been introduced by Peskin in the 70's in order to model and approximate fluid-structure interaction problems related to the blood flow in the heart. The original scheme makes use of finite differences for the discretization of the Navier-Stokes equations. Recently, a finite element formulation has been introduced which has the advantage of handling the presence of the solid (modeled via a Dirac delta function) in a more natural way. In this paper we review the finite element formulation of the IBM focusing, in particular, on the choice of the finite element spaces in order to guarantee a suitable mass conservation. Moreover, we present some links with the fictitious domain method. 
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Boffi, Daniele. The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 711-724. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a9/

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