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).

翻译：本文分析了一种基于无散混合有限元方法与连续内罚稳定化的压力鲁棒方法。主要目标是证明在对流主导区域中，速度的$L^2$范数具有$O(h^{k+1/2})$误差估计。该界具有压力鲁棒性（速度误差界不依赖于压力）和扩散鲁棒性（误差界中的常数与雷诺数无关）。