Journal of the
Korean Mathematical Society JKMS

A two-level finite element method based on the Newton iterative method is proposed for solving the Navier--Stokes/Darcy model. The algorithm solves a nonlinear system on a coarse mesh $H$ and two linearized problems of different loads on a fine mesh $h=O(H^{4-\epsilon})$. Compared with the common two-grid finite element methods for the considered problem, the presented two-level method allows for larger scaling between the coarse and fine meshes. Moreover, we prove the stability and convergence of the considered two-level method. Finally, we provide numerical experiment to exhibit the effectiveness of the presented method.

Keywords: Navier--Stokes/Darcy model, interface conditions, two-level method, Newton iteration, scaling

MSC numbers: Primary 65N30, 65N12

Supported by: The second author was supported by the Natural Science Foundation of China (grant number 11861067).