In this paper, we develop and analyze a novel numerical scheme for the steady incompressible Navier-Stokes equations by the weak Galerkin methods. The divergence-preserving velocity reconstruction operator is employed in the discretization of momentum equation. By employing the velocity construction operator, our algorithm can achieve pressure-robust, which means, the velocity error is independent of the pressure and the irrotational body force. Error analysis is established to show the optimal rate of convergence. Numerical experiments are presented to validate the theoretical conclusions.

中文翻译：

---

Navier-Stokes方程的压强弱Galerkin有限元方法

在本文中，我们通过弱Galerkin方法开发并分析了一个不可压缩的Navier-Stokes方程的新型数值格式。动量方程离散化采用了保散速度重构算子。通过使用速度构造算子，我们的算法可以实现稳健的压力，这意味着速度误差与压力和旋转力无关。建立误差分析以显示最佳收敛速度。通过数值实验验证了理论结论。