The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor-Hood (continuous P2-P1) bulk elements is proposed. A so-called volume normal derivative stabilization, known from the literature on trace FEM, is an essential ingredient of this method. The key result proved in the paper is an inf-sup stability of the trace P2-P1 finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh. Optimal order convergence of a consistent variant of the finite element method follows from this new stability result and interpolation properties of the trace FEM. Properties of the method are illustrated with numerical examples.

中文翻译：

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表面偏微分方程的迹线 $P_2-P_1$ Taylor-Hood 元素的 Inf-sup 稳定性

本文研究了一种几何未拟合的有限元方法 (FEM)，称为跟踪 FEM 或切割 FEM，用于对封闭光滑表面上的 Stokes 系统进行数值求解。提出了基于标准 Taylor-Hood（连续 P2-P1）体单元的跟踪 FEM。所谓的体积法向导数稳定，从关于痕量 FEM 的文献中得知，是该方法的基本组成部分。论文中证明的关键结果是轨迹 P2-P1 有限元对的 inf-sup 稳定性，其稳定性常数关于离散化参数和体网格中表面的位置一致有界。有限元方法的一致变体的最优阶收敛遵循这一新的稳定性结果和轨迹 FEM 的插值特性。