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<p>In this paper, two novel two-grid Uzawa methods are proposed and studied to solve the magnetohydrodynamic equations with low electromagnetic Reynolds number. These methods employ the existing modified Uzawa method to acquire the coarse grid solution, and then enhance efficiency by incorporating two distinct one-step approaches–Oseen and decoupled Oseen–on the fine grid. By combining the modified Uzawa method with the two-grid strategy, these methods retain the best features of both techniques while overcoming some of their limitations. Additionally, the error analysis of these two methods is carefully examined, and numerical experiments are reported to validate the theoretical findings and demonstrate the efficiency of the proposed methods.</p>

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Two-Grid Uzawa methods for Magnetohydrodynamic equations with low electromagnetic Reynolds number

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Yao Wang,
  • Guangzhi Du,
  • Yuhong Zhang

摘要

In this paper, two novel two-grid Uzawa methods are proposed and studied to solve the magnetohydrodynamic equations with low electromagnetic Reynolds number. These methods employ the existing modified Uzawa method to acquire the coarse grid solution, and then enhance efficiency by incorporating two distinct one-step approaches–Oseen and decoupled Oseen–on the fine grid. By combining the modified Uzawa method with the two-grid strategy, these methods retain the best features of both techniques while overcoming some of their limitations. Additionally, the error analysis of these two methods is carefully examined, and numerical experiments are reported to validate the theoretical findings and demonstrate the efficiency of the proposed methods.