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. We show a priori error estimates under additional regularity hypothesis. Moreover, the errors {in energy and $L^2$ norms for velocity and the error in $L^2$ norm for pressure} are robust with respect to the viscosity {and independent of the location of the interface}. Results of numerical experiments are presented to {support} the theoretical analysis.

翻译：在本文中,针对不要求接口与三角对映的不合格三角元素的 Stokes 界面问题,提出了稳定扩展的有限要素方法。 界面每侧的速度溶液和压力溶液分别在标准不对齐的单向线性线性多球体和单向常态多球体中分别扩大。 介面和切断边缘分别使用调和加权通量和算术通量( 介面截断的边缘部分) 。 添加涉及速度和压力的额外稳定化条件, 以确保稳定的侧向状态。 我们在附加的常规假设中显示一个先验错误估计值。 此外, 速度错误( 能源) 和 $L $2$ 标准 和 压力 $L $2$ 规范值的错误, 与介面值 { 和介面的位置无关 。 数字实验的结果被提交给 {支持} 理论分析 。