We study a higher-order surface finite-element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the choice of discretization of the diffusion term and of the divergence term on numerical accuracy and convergence, as well as on implementation advantages, is discussed. We analyze the inf-sup stability of the discrete scheme in a generic approach by lifting stable finite-element pairs known from the literature. A discretization error analysis in tangential norms then shows optimal order convergence of an isogeometric setting that requires only geometric knowledge of the discrete surface.

翻译：我们研究了切向表面Stokes问题的一种高阶表面有限元（SFEM）罚函数离散格式。本文探讨了在连续情形下等价的几种离散形式，并讨论了扩散项和散度项的不同离散化对数值精度、收敛性以及实现优势的影响。通过引入文献中已知的稳定有限元对，我们采用通用方法分析了离散格式的inf-sup稳定性。基于切向范数的离散误差分析表明，在仅需离散曲面几何信息的等几何框架下，可获得最优阶收敛性。