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.
Cite this article
Daniele Boffi, Lucia Gastaldi, Existence, uniqueness, and approximation of a fictitious domain formulation for fluid-structure interactions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 1, pp. 109–137DOI 10.4171/RLM/966