A two-level finite element method for the steady-state Navier--Stokes/Darcy model
J. Korean Math. Soc. 2020 Vol. 57, No. 4, 915-933
https://doi.org/10.4134/JKMS.j190449
Published online July 1, 2020
Jilin Fang, Pengzhan Huang, Yi Qin
Xinjiang University; Xinjiang University; Xi'an Jiaotong University
Abstract : 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).
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