Existence, uniqueness, and approximation of a fictitious domain formulation for fluid-structure interactions

TL;DR

This paper presents a comprehensive computational model for fluid-structure interactions using a fictitious domain approach, covering theoretical foundations, stability analysis, and numerical schemes.

Contribution

It advances the finite element fictitious domain method by establishing well-posedness, unconditionally stable semi-discretizations, and improved stability analysis for discretized schemes.

Findings

Well-posedness of the formulation at the continuous level.

Development of unconditionally stable semi-discrete schemes.

Enhanced stability analysis for finite element discretizations.

Abstract

In this paper we describe a computational model for the simulation of fluid-structure 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 method (FE-DLM). 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.