Quadrature error estimates on non-matching grids in a fictitious domain framework for fluid-structure interaction problems

TL;DR

This paper analyzes quadrature errors in a fictitious domain approach for fluid-structure interaction, proving well-posedness with approximate coupling matrices and providing error estimates for non-matching grids.

Contribution

It establishes the well-posedness of the discrete problem with approximate coupling and derives quadrature error estimates for non-matching grids.

Findings

Discrete problem remains well-posed with approximate coupling matrices.

Provides bounds for quadrature errors on non-matching grids.

Enhances understanding of numerical accuracy in fluid-structure simulations.

Abstract

We consider a fictitious domain formulation for fluid-structure interaction problems based on a distributed Lagrange multiplier to couple the fluid and solid behaviors. How to deal with the coupling term is crucial since the construction of the associated finite element matrix requires the integration of functions defined over non-matching grids: the exact computation can be performed by intersecting the involved meshes, whereas an approximate coupling matrix can be evaluated on the original meshes by introducing a quadrature error. The purpose of this paper is twofold: we prove that the discrete problem is well-posed also when the coupling term is constructed in approximate way and we discuss quadrature error estimates over non-matching grids.