# Higher-order time-stepping schemes for fluid-structure interaction problems

## TL;DR

This paper develops and analyzes second-order time-stepping schemes for fluid-structure interaction problems using a distributed Lagrange multiplier approach, demonstrating their stability and effectiveness through numerical tests.

## Contribution

It introduces and studies second-order time integration schemes for fluid-structure interaction using a distributed Lagrange multiplier framework, with proven stability and validated numerical results.

## Key findings

- The schemes are unconditionally stable under certain conditions.
- Numerical tests confirm the theoretical stability results.
- Second-order accuracy is achieved in fluid-structure interaction simulations.

## Abstract

We consider a recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. In this paper we focus on time integration methods of second order based on backward differentiation formulae and on the Crank-Nicolson method. We show the stability properties of the resulting method; numerical tests confirm the theoretical results.