In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and right hand side terms by using an H(div)-conforming velocity reconstruction operator. In order to match the rotation form and error analysis, a novel skew-symmetric discrete trilinear form containing the reconstruction operator is proposed, in which not only the velocity test function is changed. The corresponding well-posed discrete weak formulation stems straight from the classical inf-sup stable mixed conforming high-order finite elements, and it is proven to achieve the pressure-independent velocity errors. Optimal convergence rates of H1, L2-error for the velocity and L2-error for the Bernoulli pressure are completely established. Adequate numerical experiments are presented to demonstrate the theoretical results and the remarkable performance of the proposed method.

翻译：在这项工作中,我们为固定的不压缩纳维埃-斯托克斯方程式的旋转形式开发了一种高阶压力-气旋法。最初的想法是使用一个与H(div)相容的速度重建操作员来改变三线和右手侧条件的离散性速度测试功能。为了匹配旋转形式和错误分析,我们提出了一个包含重建操作员的新颖的对称离散三线形式,其中不仅改变了速度测试功能。相应的测得好的离散弱配方直接来自典型的异端稳定混合符合高序的定数元件,并证明它能够达到依赖压力的速度错误。H1、速度L2-error和伯努尔努利压力L2-error的优化趋同率已经完全确定。提出了适当的数字实验,以证明拟议方法的理论结果和显著表现。