We consider the surface Stokes equation on a smooth closed hypersurface in three-dimensional space. For discretization of this problem a generalization of the surface finite element method (SFEM) of Dziuk-Elliott combined with a Hood-Taylor pair of finite element spaces has been used in the literature. We call this method Hood-Taylor-SFEM. This method uses a penalty technique to weakly satisfy the tangentiality constraint. In this paper we present a discretization error analysis of this method resulting in optimal discretization error bounds in an energy norm. We also address linear algebra aspects related to (pre)conditioning of the system matrix.

翻译：本文考虑三维空间中光滑封闭超曲面上的曲面斯托克斯方程。针对该问题的离散化，现有文献已采用Dziuk-Elliott曲面有限元法（SFEM）的推广形式，并结合胡德-泰勒有限元空间对。我们将该方法称为胡德-泰勒-SFEM。该方法利用罚函数技术弱满足切向约束条件。本文对该方法进行了离散化误差分析，得到了能量范数下的最优离散化误差界。此外，我们还讨论了与系统矩阵（预）条件处理相关的线性代数方面的内容。