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摘要
In this paper, we propose a two-grid finite element method for solving the mixed Navier-Stokes/Darcy model with the Beavers-Joseph-Saffman interface condition. After solving a coupled nonlinear problem on a coarse grid, we sequentially solve decoupled and linearized subproblems on a fine grid and then correct the solution on the same grid. Compared with the existing work on the two-grid methods for the coupled model, our two-grid method allows a much higher order scaling between the coarse grid size H and 21 I = the fine grid size h. Specifically, if a k-th order discretization is applied, by using h H2k+1/k for k = 1, 2 and h = HK+1/K-1 for k >= 3, the final step two-grid solution errors in the energy norm are still optimal. Numerical experiments are also given to confirm the theoretical analysis.
