Multigoal-oriented error estimation and mesh adaptivity for fluid-structure interaction

TL;DR

This paper develops a multigoal-oriented error estimation method for stationary fluid-structure interaction problems, enabling simultaneous control of multiple quantities of interest through advanced mesh adaptivity techniques.

Contribution

It introduces a combined goal-oriented error estimation approach using dual-weighted residuals for FSI problems within a variational-monolithic framework.

Findings

Effective mesh refinement for multiple goals demonstrated in numerical tests.

Accurate control of several quantities of interest achieved.

Method applicable to complex FSI benchmark problems.

Abstract

In this work, we consider multigoal-oriented error estimation for stationary fluid-structure interaction. The problem is formulated within a variational-monolithic setting using arbitrary Lagrangian-Eulerian coordinates. Employing the dual-weighted residual method for goal-oriented a posteriori error estimation, adjoint sensitivities are required. For multigoal-oriented error estimation, a combined functional is formulated such that several quantities of interest are controlled simultaneously. As localization technique for mesh refinement we employ a partition-of-unity. Our algorithmic developments are substantiated with several numerical tests such as an elastic lid-driven cavity with two goal functionals, an elastic bar in a chamber with two goal functionals, and the FSI-1 benchmark with three goal functionals.