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In this paper, a stabilized extended finite element method is proposed forStokes interface problems on unfitted triangulation elements which do notrequire the interface align with the triangulation. The velocity solution andpressure solution on each side of the interface are separately expanded in thestandard nonconforming piecewise linear polynomials and the piecewise constantpolynomials, respectively. Harmonic weighted fluxes and arithmetic fluxes areused across the interface and cut edges (segment of the edges cut by theinterface), respectively. Extra stabilization terms involving velocity andpressure are added to ensure the stable inf-sup condition. We show a priorierror estimates under additional regularity hypothesis. Moreover, the errors{in energy and $L^2$ norms for velocity and the error in $L^2$ norm forpressure} are robust with respect to the viscosity {and independent of thelocation of the interface}. Results of numerical experiments are presented to{support} the theoretical analysis.

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