This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and the pressure space consists of piecewise linear polynomials without continuity constraints. A Lagrange multiplier space that consists of continuous piecewise quadratic polynomials with respect to boundary partition is introduced to enforce boundary conditions as well as to mitigate the lack of pressure-robustness. We prove several inf-sup conditions, leading to the well-posedness of the method. In addition, we show that the method converges with optimal order and the velocity approximation is divergence free.

翻译：本文根据Clough- Tocher 分割上的 Scott- Vogelius 配对, 构建并分析了 Stokes 问题的边界校正有限元素方法。 速度空间由连续的片断四面形多面体组成, 压力空间由无连续性限制的片断线性多面体组成。 引入了由连续的片断四面形多面体组成的拉格朗增殖空间, 以强制实施边界条件, 并减轻压力- 温度的缺乏。 我们证明了一些内溢条件, 导致该方法的稳妥性。 此外, 我们展示了该方法与最佳顺序的趋同, 且速度逼近是自由差异的 。