A fictitious domain approach with distributed Lagrange multiplier for fluid-structure interactions

TL;DR

This paper presents a novel fictitious domain approach with distributed Lagrange multipliers for fluid-structure interactions, including stability analysis and optimal convergence proofs for finite element discretizations.

Contribution

It introduces a new formulation for fluid-structure interaction problems using distributed Lagrange multipliers, with rigorous stability and convergence analysis.

Findings

Proves stability of the proposed formulation.

Establishes optimal convergence estimates for finite element discretization.

Provides a rigorous mathematical foundation for the method.

Abstract

We study 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. The time discretization of the problem leads to a mixed problem for which a rigorous stability analysis is provided. The finite element space discretization is discussed and optimal convergence estimates are proved.