In this paper, we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm of the velocity in the convection dominated regime. This bound is pressure robust (the error bound of the velocity does not depend on the pressure) and also convection robust (the constants in the error bounds are independent of the Reynolds number).

中文翻译：

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不可压缩纳维-斯托克斯方程连续内罚散度有限元法的压力和对流鲁棒边界

在本文中，我们分析了一种基于连续内罚稳定的无散混合有限元方法的压力鲁棒方法。主要目标是证明对流主导区域中速度 $L^2$ 范数的 $O(h^{k+1/2})$ 误差估计。该界限具有压力鲁棒性（速度的误差界限不依赖于压力）并且对流鲁棒性（误差界限中的常数与雷诺数无关）。