An unfitted Nitsche method for incompressible fluid–structure interaction using overlapping meshes

We consider the extension of the Nitsche method to the case of fluid–structure interaction problems on unfitted meshes. We give a stability analysis for the space semi-discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions, irrespectively of the mesh/interface intersection. We also discuss different strategies for the time discretization, using either fully implicit or explicit coupling (loosely coupled) schemes. Some numerical examples illustrate the theoretical discussion. •Unfitted finite element method for a fluid–structure interaction.•Proof of stability and accuracy.•Different coupling scheme’s for time advancement: fully coupled or loosely coupled.