Two-level Newton iterative method for the 2D/3D steady Navier-Stokes equations

Authors

  • Yinnian He,

    Corresponding author
    1. Faculty of Science, State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
    • Faculty of Science, State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
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  • Yan Zhang,

    1. Faculty of Science, State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
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  • Yueqiang Shang,

    1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, People's of Republic of China
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  • Hui Xu

    1. School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
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Abstract

A combination method of the Newton iteration and two-level finite element algorithm is applied for solving numerically the steady Navier-Stokes equations under the strong uniqueness condition. This algorithm is motivated by applying the m Newton iterations for solving the Navier-Stokes problem on a coarse grid and computing the Stokes problem on a fine grid. Then, the uniform stability and convergence with respect to ν of the two-level Newton iterative solution are analyzed for the large m and small H and h << H. Finally, some numerical tests are made to demonstrate the effectiveness of the method. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

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