Finite elements for fluid–structure interaction in ALE and fully Eulerian coordinates

In this work we describe and compare two monolithic models for fluid–structure interaction problems: First, the well-established ALE model using natural Lagrangian coordinates for the structural model and using an artificial coordinate system for the flow problem. Then, a novel approach, the fully Eulerian coordinates, where both subproblems, structure and fluid are given in Eulerian coordinates. The approaches have in common that a closed variational formulation exists. This allows the use of implicit solution schemes, goal oriented error estimation and gradient based optimization algorithms. this work is the introduction and verification of the novel fully Eulerian model for stationary fluid–structure interaction problems.