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