  We present a monolithic finite element formulation for (nonlinear)
fluid-structure interaction in Eulerian coordinates. For the discretization we
employ an unfitted finite element method based on inf-sup stable finite
elements. So-called ghost penalty terms are used to guarantee the robustness of
the approach independently of the way the interface cuts the finite element
mesh. The resulting system is solved in a monolithic fashion using Newton's
method. Our developments are tested on a numerical example with fixed
interface.
