A Nitsche-based cut finite element method for a fluid-structure interaction problem

We present a new composite mesh finite element method for fluid-structure interaction problems.The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh.The embedding allows for an arbitrary overlap of the fluid meshes.The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates.We consider here a steady state fluid-structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations.We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.