Goal-oriented error estimation for fluid–structure interaction problems

In this work, we present an adaptive finite element method for the numerical simulation of stationary fluid–structure interaction problems. The coupled system is given in a variational and monolithic Arbitrary Lagrangian Eulerian framework. We derive methods for goal-oriented error estimation and mesh adaptation with the dual weighted residual method. Key to applying this error estimator is the underlying canonic variational formulation of the fluid–structure interaction problem by mapping the flow problem to ALE coordinates. The developed method is applied to two and three dimensional stationary benchmark problems coupling the incompressible Navier–Stokes equations with a nonlinear hyper-elastic material law.