  This paper studies a model of two-phase flow with an immersed material
viscous interface and a finite element method for numerical solution of the
resulting system of PDEs. The interaction between the bulk and surface media is
characterized by no-penetration and slip with friction interface conditions.
The system is shown to be dissipative and a model stationary problem is proved
to be well-posed. The finite element method applied in this paper belongs to a
family of unfitted discretizations. The performance of the method when model
and discretization parameters vary is assessed. Moreover, an iterative
procedure based on the splitting of the system into bulk and surface problems
is introduced and studied numerically.
