In this paper, we design and analyze staggered discontinuous Galerkin methods of arbitrary polynomial orders for the stationary Navier-Stokes equations on polygonal meshes. The exact divergence-free condition for the velocity is satisfied without any postprocessing. The resulting method is pressure-robust so that the pressure approximation does not influence the velocity approximation. A new nonlinear convective term that earning non-negativity is proposed. The optimal convergence estimates for all the variables in $L^2$ norm are proved. Also, assuming that the rotational part of the forcing term is small enough, we are able to prove that the velocity error is independent of the Reynolds number and of the pressure. Furthermore, superconvergence can be achieved for velocity under a suitable projection. Numerical experiments are provided to validate the theoretical findings and demonstrate the performances of the proposed method.

翻译：在本文中, 我们设计并分析对多边形网外的固定纳维埃- 斯托克斯方程式任意的不连续的加列金方法。 速度的完全无差异性条件在没有任何后处理的情况下得到满足。 由此产生的方法是压力- 气压粗压, 使压近似不会影响速度近似。 提出了一个新的非线性对流术语, 即: 得出非负负值。 证明了所有变量在 $L2$ 标准中的最佳趋同估计值。 另外, 假设强制期的旋转部分足够小, 我们就能证明速度错误独立于雷诺兹的数字和压力。 此外, 在适当的预测下, 速度可以实现超趋同。 提供数字实验, 以验证理论结果并展示拟议方法的性能。