In this paper, we propose a nonconforming extended virtual element method, which combines the extended finite element method with the nonconforming virtual element method, for solving Stokes interface problems with the unfitted-interface mesh. By introducing some stabilization terms and penalty terms, as well as some special terms defined on non-cut edges of interface elements in the discrete bilinear form, we prove the discrete inf-sup condition and obtain optimal error estimates. It is shown that all results are not only independent of the mesh size and the viscosity coefficient, but also the interface position. Numerical experiments are performed to verify theoretical results.

中文翻译：

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用于 Stokes 接口问题的不合规扩展虚拟元方法


在本文中，我们提出了一种非共形扩展虚元方法，该方法将扩展有限元法与非共形虚元法相结合，用于求解未拟合界面网格的斯托克斯界面问题。通过引入一些稳定项和罚项，以及在离散双线性形式的界面单元的非切割边缘上定义的一些特殊项，我们证明了离散 inf-sup 条件并获得了最优误差估计。结果表明，所有结果不仅与网格大小和粘度系数无关，而且与界面位置无关。进行数值实验以验证理论结果。