Advances on the finite element discretization of fluid-structure interaction problems
arXiv:2505.02594 · doi:10.1007/s40065-025-00570-8
Abstract
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical findings concerning well-posedness, stability, and convergence of the numerical schemes, and discuss the related computational challenges. In the case of elliptic interface problems, we also present a posteriori error estimates.
30 pages, 12 figures, 3 tables