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Uniform Stability and Convergence with Respect to \((\nu , \mu , s, 1-\sigma )\) of the Three Iterative Finite Element Solutions for the 3D Steady MHD Equations

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Abstract

In this paper, the Stokes, Newton and Oseen iterative finite element methods are presented for the 3D steady MHD equations. These methods consist of approximating the solution pair ((u, B), p) of the 3D steady MHD equations by combining the Stokes, Newton and Oseen iterative methods with the finite element method. The uniform stability and convergence results with respect to \((\nu , \mu , s,1-\sigma )\) of the three iterative finite element solutions \(((u^n_h,B_h^n),p_h^n)\) under the convergence conditions are provided. Finally, some numerical tests are presented to show the efficiency of the numerical analysis results for the present iterative finite element methods on the 3D steady MHD equations.

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Acknowledgements

The research was supported by the National Natural Science Foundation of China (Nos:11771348,12071404,11701151), the Natural Science Foundation of Hunan Province (No: 2019JJ40279), Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education (Nos:20B564,18B064), China Postdoctoral Science Foundation (Nos: 2018T110073, 2018M631402), International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science (No: 2018WK4006).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinnian He

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent, Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Xiaojing Dong

  3. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Xinlong Feng

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  1. Yinnian He
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  2. Xiaojing Dong
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Correspondence to Xiaojing Dong.

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He, Y., Dong, X. & Feng, X. Uniform Stability and Convergence with Respect to \((\nu , \mu , s, 1-\sigma )\) of the Three Iterative Finite Element Solutions for the 3D Steady MHD Equations. J Sci Comput 90, 17 (2022). https://doi.org/10.1007/s10915-021-01671-0

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  • DOI: https://doi.org/10.1007/s10915-021-01671-0

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