In this paper, we develop and study the mixed finite element method for a hemivariational inequality of the stationary Navier–Stokes equations (NS hemivariational inequality). The NS hemivariational inequality models the motion of a viscous incompressible fluid in a bounded domain, subject to a nonsmooth and nonconvex slip boundary condition. The incompressibility contraint is treated through a mixed formulation. Solution existence and uniqueness are explored. The mixed finite element method is applied to solve the NS hemivariational inequality and error estimates are derived. Numerical results are reported on the use of the P1b/P1 pair, illustrating the optimal convergence order predicted by the error analysis.

在本文中，我们开发并研究了固定 Navier-Stokes 方程的半变分不等式（NS 半变分不等式）的混合有限元方法。NS 半变分不等式模拟粘性不可压缩流体在有界域中的运动，受非光滑和非凸滑动边界条件的影响。不可压缩性约束通过混合配方进行处理。探索解决方案的存在性和唯一性。应用混合有限元法求解NS半变分不等式，推导出误差估计。报告了使用 P1b/P1 对的数值结果，说明了误差分析预测的最佳收敛顺序。