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An efficient decoupled finite element scheme for the incompressible hall magnetohydrodynamics equations

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  • Wei, Xiaojing
  • Mei, Liquan

Abstract

This study is dedicated to developing and analyzing of a numerical scheme for the incompressible Hall Magnetohydrodynamics equations in three dimensions, with a focus on second-order time accuracy, full decoupling, linearization, and unconditional energy stability. In this paper, we construct a finite element scheme that meets the above requirements. The scheme combines the pressure projection method with the “zero energy contribution” feature of nonlinear terms, which not only guarantees the second-order time accuracy, but also fully decouples the equations. Furthermore, the explicit treatment of nonlinear terms simplifies the computational complexity. To verify the effectiveness of the proposed scheme, we theoretically prove the well-posedness and unconditional energy stability, and conduct extensive numerical experiments. These results show that the proposed scheme has strong theoretical properties, performs effectively in practical applications, and can effectively solve the complex problems caused by the introduction of Hall term in Magnetohydrodynamics equations.

Suggested Citation

  • Wei, Xiaojing & Mei, Liquan, 2026. "An efficient decoupled finite element scheme for the incompressible hall magnetohydrodynamics equations," Applied Mathematics and Computation, Elsevier, vol. 514(C).
    • Handle: RePEc:eee:apmaco:v:514:y:2026:i:c:s0096300325005387
    DOI: 10.1016/j.amc.2025.129813
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    References listed on IDEAS

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    1. Wang, Weilong, 2023. "Novel pressure-correction schemes based on scalar auxiliary variable method for the MHD equations," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    2. Fan, Jishan & Ahmad, Bashir & Hayat, Tasawar & Zhou, Yong, 2016. "On blow-up criteria for a new Hall-MHD system," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 20-24.
    3. Yuan, Baoquan & Li, Chaoying, 2019. "The 3D incompressible Hall magneto-hydrodynamics equations with partial hyperdissipation," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 308-332.
    4. Ye, Zhuan & Zhang, Zujin, 2017. "A remark on regularity criterion for the 3D Hall-MHD equations based on the vorticity," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 70-77.
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