We study a higher-order surface finite-element 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 analyse 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.

中文翻译：

---

表面的参数有限元离散化 Stokes 方程：inf-sup 稳定性和离散化误差分析


我们研究了切向表面 Stokes 问题的高阶表面有限元基于罚的离散化。研究了几种离散公式，它们在连续设置中是等效的。讨论了扩散项和散度项的离散化选择对数值精度和收敛性以及实施优势的影响。我们通过提取文献中已知的稳定有限元对，以通用方法分析离散方案的 inf-sup 稳定性。然后，切向范数中的离散化误差分析显示了等几何设置的最佳阶收敛性，该设置只需要离散表面的几何知识。