Advances on the finite element discretization of fluid-structure interaction problems

TL;DR

This paper reviews an unfitted finite element method for fluid-structure interaction problems, highlighting theoretical properties, computational challenges, and error estimates, advancing numerical techniques for complex interface problems.

Contribution

It introduces a finite element approach based on a distributed Lagrange multiplier, with proven well-posedness, stability, convergence, and error estimation for interface problems.

Findings

Proven well-posedness, stability, and convergence of the method.

Development of a posteriori error estimates for elliptic interface problems.

Discussion of computational challenges in implementing the method.

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.