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Newton Iterative Parallel Finite Element Algorithm for the Steady Navier-Stokes Equations

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Abstract

A combination method of the Newton iteration and parallel finite element algorithm is applied for solving the steady Navier-Stokes equations under the strong uniqueness condition. This algorithm is motivated by applying the Newton iterations of m times for a nonlinear problem on a coarse grid in domain Ω and computing a linear problem on a fine grid in some subdomains Ω j ⊂Ω with j=1,…,M in a parallel environment. Then, the error estimation of the Newton iterative parallel finite element solution to the solution of the steady Navier-Stokes equations is analyzed for the large m and small H and h≪H. Finally, some numerical tests are made to demonstrate the the effectiveness of this algorithm.

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Authors and Affiliations

  1. Faculty of Science, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Yinnian He, Liquan Mei & Juan Cui

  2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, P.R. China

    Yueqiang Shang

Authors
  1. Yinnian He
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  2. Liquan Mei
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  3. Yueqiang Shang
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  4. Juan Cui
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Correspondence to Yinnian He.

Additional information

The first author was partially subsidized by the NSFs of China (No. 10971166 and 10971164) and the National Basic Research Program (No. 2005CB321703); the third author was subsidized by the Science and Technology Foundation of Guizhou Province, China (No. [2008]2123).

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He, Y., Mei, L., Shang, Y. et al. Newton Iterative Parallel Finite Element Algorithm for the Steady Navier-Stokes Equations. J Sci Comput 44, 92–106 (2010). https://doi.org/10.1007/s10915-010-9371-4

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  • DOI: https://doi.org/10.1007/s10915-010-9371-4

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