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：本文提出了一种适用于几何非拟合有限元方法，用于数值求解嵌入$\mathbb{R}^3$中被动演化光滑闭曲面上的切向Navier-Stokes方程。离散公式采用有限差分法处理时间演化，有限元法处理空间变化。本文对该方法进行了完整的数值分析，包括稳定性、最优阶收敛性以及几何误差的量化，并给出了数值实验的结果。