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

<p style='text-indent:20px;'>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 problem is written on mixed form using nonconforming <inline-formula><tex-math id="M1">\begin{document}$ P_1 $\end{document}</tex-math></inline-formula> velocity and elementwise <inline-formula><tex-math id="M2">\begin{document}$ P_0 $\end{document}</tex-math></inline-formula> pressure. Extra stabilization terms involving velocity and pressure are added in the discrete bilinear form. An inf-sup stability result is derived, which is uniform with respect to mesh size <inline-formula><tex-math id="M3">\begin{document}$ h $\end{document}</tex-math></inline-formula>, the viscosity and the position of the interface. An optimal priori error estimates are obtained. Moreover, the errors in energy norm for velocity and in <inline-formula><tex-math id="M4">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> norm for pressure are uniform to the viscosity and the location of the interface. Results of numerical experiments are presented to support the theoretical analysis.</p>