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Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

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Abstract

This paper presents an anisotropic adaptive finite element method (FEM) to solve the governing equations of steady magnetohydrodynamic (MHD) duct flow. A residual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu estimates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Jikun Zhao

  2. State Key Laboratory of Scientific and Engineering Computing (LSEC) and Institute of Computational Mathematics, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, Beijing, 100190, China

    Shipeng Mao & Weiying Zheng

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    Shipeng Mao & Weiying Zheng

Authors
  1. Jikun Zhao
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  2. Shipeng Mao
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  3. Weiying Zheng
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Corresponding author

Correspondence to Shipeng Mao.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11471329, 11321061, and 91430215), the National Magnetic Confinement Fusion Science Program of China (No. 2015GB110000), the Youth Innovation Promotion Association of Chinese Academy of Sciences (CAS) (No. 2016003), and the National Center for Mathematics and Interdisciplinary Sciences of CAS

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Zhao, J., Mao, S. & Zheng, W. Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers. Appl. Math. Mech.-Engl. Ed. 37, 1479–1500 (2016). https://doi.org/10.1007/s10483-016-2107-9

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  • DOI: https://doi.org/10.1007/s10483-016-2107-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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