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<p>This paper mainly presents and studies some local and parallel finite element methods for the unsteady magnetohydrodynamic equations with low electromagnetic Reynolds number. Firstly, both the semi discrete and fully discrete local algorithms are provided and investigated, and the theoretical tool crucial to the analysis of the fully discrete local algorithm is obtained. Subsequently, we generalize the fully discrete local algorithm to the fully discrete parallel algorithm. At the end, some numerical experiments are provided to validate the effectiveness and efficiency of our algorithms.</p>

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Local and Parallel Finite Element Algorithms Based on Two-grid Discretizations for the Unsteady MHD Equations with Low Electromagnetic Reynolds Number

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Shi-lin Mi,
  • Guang-zhi Du,
  • Yao Rong,
  • Li-yun Zuo

摘要

This paper mainly presents and studies some local and parallel finite element methods for the unsteady magnetohydrodynamic equations with low electromagnetic Reynolds number. Firstly, both the semi discrete and fully discrete local algorithms are provided and investigated, and the theoretical tool crucial to the analysis of the fully discrete local algorithm is obtained. Subsequently, we generalize the fully discrete local algorithm to the fully discrete parallel algorithm. At the end, some numerical experiments are provided to validate the effectiveness and efficiency of our algorithms.