The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori estimates for the individual terms of the Cauchy stress tensor with stability constants independent of the viscosity coefficient. Next, this stability result is extended to the approximation of the two-phase Stokes problem by a finite element method. In the method considered, the interface between the phases does not respect the underlying triangulation, which put the finite element method into the class of unfitted discretizations. The finite element error estimates are proved with constants independent of viscosity. Numerical experiments supporting the theoretical results are provided.

中文翻译：

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两相斯托克斯问题未拟合有限元方法的新稳定性估计

该论文解决了固定两相斯托克斯问题的稳定性和有限元分析，其中分段恒定粘度系数在两个流体相之间的界面上发生跳跃。我们首先证明了柯西应力张量的各个项的先验估计，其稳定性常数与粘度系数无关。接下来，该稳定性结果通过有限元方法扩展到两相斯托克斯问题的近似。在所考虑的方法中，相之间的界面不考虑潜在的三角剖分，这将有限元方法置于未拟合离散化的类别中。用与粘度无关的常数证明了有限元误差估计。提供了支持理论结果的数值实验。