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http://dx.doi.org/10.4134/JKMS.j190449

A TWO-LEVEL FINITE ELEMENT METHOD FOR THE STEADY-STATE NAVIER-STOKES/DARCY MODEL  

Fang, Jilin (College of Mathematics and System Sciences Xinjiang University)
Huang, Pengzhan (College of Mathematics and System Sciences Xinjiang University)
Qin, Yi (School of Mathematics and Statistics Xi'an Jiaotong University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 915-933 More about this Journal
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(H4-𝜖). 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;
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Times Cited By KSCI : 2  (Citation Analysis)
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