  In this paper we describe a computational model for the simulation of
fluid-structure interaction problems based on a fictitious domain approach. We
summarize the results presented over the last years when our research evolved
from the Finite Element Immersed Boundary Method (FE-IBM) to the actual Finite
Element Distributed Lagrange Multiplier method (FE-DLM). We recall the
well-posedness of our formulation at the continuous level in a simplified
setting. We describe various time semi-discretizations that provide
unconditionally stable schemes. Finally we report the stability analysis for
the finite element space discretization where some improvements and
generalizations of the previous results are obtained.
