Stability and error estimates of a linear and partitioned finite element method approximating nonlinear fluid-structure interactions

TL;DR

This paper introduces and analyzes a stable, partitioned finite element method for nonlinear fluid-structure interactions, providing theoretical error estimates validated by numerical experiments.

Contribution

It presents a novel linear, partitioned FEM approach for fluid-shell interactions under ALE, with stability and error analysis without simplifying assumptions.

Findings

Proves stability and error estimates for the proposed scheme.

Demonstrates convergence through numerical experiments.

Handles nonlinear fluid-structure interactions without neglecting fluid convection.

Abstract

We propose and analyze a linear and partitioned finite element method for fluid-shell interactions under the arbitrary Lagrangian-Eulerian (ALE) framework. We adopt the P1-bubble/P1/P1 elements for the fluid velocity, pressure, and structure velocity, respectively. We show the stability and error estimates of the scheme without assuming infinitesimal structural deformation nor neglecting fluid convection effects. The theoretical convergence rate is further corroborated by numerical experiments.