Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.06.30
  • Accepted : 2020.02.13
  • Published : 2020.07.01
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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.

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References

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