Based on finite element discretization and a fully overlapping domain decomposition, we propose and study some parallel iterative subgrid stabilized algorithms for the simulation of the steady Navier-Stokes equations with high Reynolds numbers, where the quadratic equal-order elements are used for the velocity and pressure approximations, and the subgrid-scale model based on an elliptic projection is employed to penalize instability introduced by the dominant convective term in the Navier-Stokes system. In the present algorithms, each subproblem is defined in the whole domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems. All of the subproblems are nonlinear and are independently solved by some iterative methods. Stability and convergence of the proposed parallel iterative algorithms are analyzed under some (strong) uniqueness conditions. Furthermore, new results of stopping criteria for nonlinear iterations are derived. Numerical examples which verify the effectiveness of the proposed algorithms are given.

基于有限元离散化和完全重叠域分解，我们提出并研究了一些并行迭代亚网格稳定算法，用于模拟具有高雷诺数的稳态Navier-Stokes方程，其中二次等阶元用于速度和压力近似，并采用基于椭圆投影的亚网格尺度模型来惩罚由 Navier-Stokes 系统中的主要对流项引入的不稳定性。在本算法中，每个子问题都在整个域中定义，其中绝大多数自由度与其负责的特定子域相关联，因此可以与其他子问题并行求解。所有子问题都是非线性的，并且可以通过一些迭代方法独立求解。在一些（强）唯一性条件下分析了所提出的并行迭代算法的稳定性和收敛性。此外，还导出了非线性迭代停止准则的新结果。给出了验证所提出算法有效性的数值例子。