We develop two unfitted finite element methods for the Stokes equations based
on Hdiv-conforming finite elements. The first method is a
cut finite element discretization of the Stokes equations based on the
Brezzi-Douglas-Marini elements and involves interior penalty terms to enforce
tangential continuity of the velocity at interior edges in the mesh. The second
method is a cut finite element discretization of a three-field formulation of
the Stokes problem involving the vorticity, velocity, and pressure and uses the
Raviart-Thomas space for the velocity. We present mixed ghost penalty
stabilization terms for both methods so that the resulting discrete problems
are stable and the divergence-free property of the
Hdiv-conforming elements is preserved also for unfitted
meshes. We compare the two methods numerically. Both methods exhibit robust
discrete problems, optimal convergence order for the velocity, and pointwise
divergence-free velocity fields, independently of the position of the boundary
relative to the computational mesh