A two-level finite element method for the steady-state Navier--Stokes/Darcy model
J. Korean Math. Soc.
Published online March 6, 2020
Jilin Fang, Pengzhan Huang, and Yi Qin
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 $h=O(H^{4-\varepsilon})$. 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,p Newton iteration, Scaling
MSC numbers : 65N30, 65N12
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