Existence, uniqueness, and approximation of a fictitious domain formulation for fluid-structure interactions

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