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：本文研究基于罚函数的高阶表面有限元（SFEM）对切向表面斯托克斯问题的离散化方法。我们探讨了若干种在连续设定下等价的离散格式，并讨论了扩散项与散度项的离散化选择对数值精度、收敛性以及实现优势的影响。通过提升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。随后在切向范数下进行的离散误差分析表明，等几何设定在仅需离散表面几何信息的情况下即可获得最优阶收敛性。