In this paper, we propose two novel Robin-type domain decomposition methods based on the two-grid techniques for the coupled Stokes–Darcy system. Our schemes firstly adopt the existing Robin-type domain decomposition algorithm to obtain the coarse grid approximate solutions. Then two one-step modified domain decomposition methods are further constructed on the fine grid by utilizing the framework of two-grid methods to enhance computational efficiency, via replacing some interface terms with the coarse grid information. The natural idea of using the two-grid frame to optimize the domain decomposition method inherits the best features of both methods and can overcome some of the domain decomposition deficits. The resulting schemes can be implemented easily using many existing mature solvers or codes in a flexible way, which are much effective under smaller mesh sizes or some realistic physical parameters. Moreover, several error estimates are carried out to show the stability and convergence of the schemes. Finally, three numerical experiments are performed and compared with the classical two-grid method, which verifies the validation and efficiency of the proposed algorithms.

在本文中，我们提出了两种新颖的罗宾型域分解方法基于耦合斯托克斯-达西系统的双网格技术。我们的方案首先采用现有的罗宾型域分解算法来获得粗网格近似解。然后在细网格上进一步构建两种一步修正域分解方法，利用两网格方法的框架，通过用粗网格信息替换一些界面项来提高计算效率。使用双网格框架优化域分解方法的自然思想继承了两种方法的最佳特征，并且可以克服一些域分解缺陷。可以使用许多现有的成熟求解器或代码以灵活的方式轻松实现所产生的方案，这些方案在较小的网格尺寸或一些实际物理参数下非常有效。而且，进行了几个误差估计以显示方案的稳定性和收敛性。最后，进行了三个数值实验，并与经典的双网格方法进行了比较，验证了所提出算法的有效性和有效性。