Combining the quadratic equal-order stabilized method with the approach of local and parallel finite element computations and classical iterative methods for the discretization of the steady-state Navier–Stokes equations, three parallel iterative stabilized finite element methods based on fully overlapping domain decomposition are proposed and compared in this paper. In these methods, each processor independently computes an approximate solution in its own subdomain using a global composite mesh that is fine around its own subdomain and coarse elsewhere, making the methods be easy to implement based on existing codes and have low communication complexity. Under some (strong) uniqueness conditions, stability and convergence theory of the parallel iterative stabilized methods are derived. Numerical tests are also performed to demonstrate the stability, convergence orders and high efficiency of the proposed methods.

结合二次等阶稳定方法与局部和并行有限元计算方法以及经典迭代方法对稳态Navier-Stokes方程进行离散化，提出了基于完全重叠域分解的三种并行迭代稳定有限元方法并在本文中进行了比较。在这些方法中，每个处理器都使用一个全局复合网格在其自己的子域中独立计算一个近似解，该网格在其自己的子域周围很好，而在其他地方则很粗糙，从而使这些方法易于基于现有代码实现且通信复杂度低。在某些（强）唯一性条件下，推导了并行迭代稳定方法的稳定性和收敛性理论。