中文摘要：

本文研究耦合Navier-Stokes/Darcy模型问题.构造一种从粗网格到细网格的有限元空间插值方法,不但简化了数值积分的单元匹配,也保证了数值积分的精度.利用基于有限元空间的多重网格方法,获得与直接法求解耦合问题误差相同的收敛阶,推广两重网格方法的结果.

英文摘要：

In this paper,we introduce and analyze numerical methods for a coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media.Based on the decoupled two-gird algorithm,we discuss the numerical implementation with the MINI elements in the triangulation and with the Q2-Q1 elements in the quadrangulation,respectively.Moreover,the corresponding multi-grid algorithm is also proposed and the error produced in the computation is given.Numerical experiments show the efficiency of the algorithm for solving the coupled problem.