The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided.

翻译：本文提出一种几何非拟合有限元方法，用于数值求解嵌入$\mathbb{R}^3$中被动演化光滑封闭曲面上的切向Navier-Stokes方程。该离散格式分别采用有限差分法和有限元法处理时间演化与空间变化。文中给出了该方法的完整数值分析，包括稳定性、最优阶收敛性以及几何误差的量化，同时提供了数值实验的结果。