Based on a fully overlapping domain decomposition approach and a recent variational multiscale method, a parallel finite element variational multiscale method for the Navier-Stokes equations with nonlinear slip boundary conditions is proposed and analyzed. In this parallel method, a global composite grid is used to find a stabilized finite element solution for each subproblem, where a stabilization term based on two local Gauss integrations at the element level is employed to stabilize the system. Using the technical tool of local a priori estimate for the finite element solution, error estimates in $H^1$-norm of velocity and $L^2$-norm of pressure are derived. Numerical results are given to verify the validity of the theoretical predictions and illustrate the high efficiency of the proposed method.

基于完全重叠域分解方法和最近的变分多尺度方法，提出并分析了具有非线性滑动边界条件的Navier-Stokes方程的并行有限元变分多尺度方法。在这种并行方法中，使用全局复合网格为每个子问题找到稳定的有限元解，其中使用基于单元级两个局部高斯积分的稳定项来稳定系统。使用有限元解的局部先验估计技术工具，在$H^1$-速度范数和 ${升}^2$- 推导出压力范数。数值结果验证了理论预测的有效性，并说明了所提出方法的高效率。