In this paper, we describe a computational model for the simulation of fluidstructure 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 (FEDLM) method. 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.
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