We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip between phases. For the unfitted generalized Taylor--Hood finite element pair $\mathbf{P}_{k+1}-P_k$, $k\ge1$, we show an inf-sup stability property with a stability constant that is independent of the viscosity ratio, slip coefficient, position of the interface with respect to the background mesh and, of course, mesh size. In addition, we prove stability and optimal error estimates that follow from this inf-sup property. We provide numerical results in two and three dimensions to corroborate the theoretical findings and demonstrate the robustness of our approach with respect to the contrast in viscosity, slip coefficient value, and position of the interface relative to the fixed computational mesh.
翻译：我们展示了CutFEM或Nitsche-XFEM家族的不相宜的参数性要素方法,用于模拟两阶段的相向问题,在两个阶段之间出现偏差。对于不相容的通用的泰勒-胡德元素元素对价$\mathbf{P ⁇ k+1}-P_k$, $k\ge1$,我们展示了一个内向稳定属性,其稳定性常数独立于粘结率、滑动系数、界面相对于背景网格的位置,当然还有网格大小。此外,我们证明了这一隐形属性的稳定性和最佳误差估计。我们提供了两个和三个层面的数字结果,以证实理论结论,并表明我们的方法在相对固定计算网格的粘结度、滑动系数值和界面位置的对比方面是稳健健的。
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