A cut finite element method for a Stokes interface problem

• Immiscible fluids with different viscosities and surface tension.
• Interface separating the fluids does not need to align with the mesh.
• Nitsche formulation allowing for discontinuous solutions and optimal error estimates.
• Stabilization method ensuring a well conditioned discrete problem.

We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We propose a Nitsche formulation which allows for discontinuities along the interface with optimal a priori error estimates. A stabilization procedure is included which ensures that the method produces a well conditioned stiffness matrix independent of the location of the interface.