Stabilized nonconforming Nitsche's extended finite element method for Stokes interface problems

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure solution on each side of the interface are separately expanded in the standard nonconforming piecewise linear polynomials and the piecewise constant polynomials, respectively. Harmonic weighted fluxes and arithmetic fluxes are used across the interface and cut edges (segment of the edges cut by the interface), respectively. Extra stabilization terms involving velocity and pressure are added to ensure the stable inf-sup condition. It is proved that the convergence orders of error estimates are optimal. Moreover, the errors are robust with respect to the viscosity. Results of numerical experiments are presented to verify the theoretical analysis.