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A Voigt Regularization for Incompressible MHD Equations in Elsässer Variables

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Abstract

A Voigt regularization is considered for the incompressible MHD equations in Elsässer variables. Then based on the BDF2, we propose and analyze a linearized and unconditionally stable finite element algorithm for this problem, which can be decoupled when the regularization parameters are equal. With the help of the Voigt regularization, the present algorithm removes the restriction involving the kinematic viscosity \(\nu \) and magnetic permeability \(\nu _m\), \(\frac{1}{2}< \nu /\nu _m< 2\), which comes from the BDF2 for the MHD equations in Elsässer variables. Furthermore, the unconditionally stability and convergence of this algorithm for the Voigt regularization of MHD equations in Elsässer variables are proved. Finally, several numerical simulations are provided to confirm the numerical theory, and show that the proposed algorithm outperforms the usual BDF2 for the problem outside the interval.

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Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions, which have led to a considerable improvement in the current work.

Funding

This work is sponsored by the Natural Science Foundation of China (grant number 12361077), Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant number 2023D14014) and the Tianshan Talent Training Program of Xinjiang Uygur Autonomous Region (grant number 2023TSYCCX0103).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830017, People’s Republic of China

    Xingwei Yang, Pengzhan Huang & Yinnian He

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

    Yinnian He

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Correspondence to Pengzhan Huang.

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Yang, X., Huang, P. & He, Y. A Voigt Regularization for Incompressible MHD Equations in Elsässer Variables. J Sci Comput 103, 21 (2025). https://doi.org/10.1007/s10915-025-02849-6

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