In this paper, we study a fully discrete vector penalty-projection method for the time-dependent incompressible magnetohydrodynamics flows. This fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization and first-order backward Euler for temporal discretization. Moreover, unconditionally energy stable is established, and error estimates for the fully discrete scheme is also derived. Finally, some numerical experiments are provided to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

中文翻译：

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时间相关不可压缩磁流体动力学流的矢量惩罚投影方法

在本文中，我们研究了时间相关不可压缩磁流体动力学流的完全离散向量惩罚投影方法。这种完全离散的方案是用于空间离散化的混合有限元近似和用于时间离散化的一阶后向欧拉的组合。此外，建立了无条件能量稳定，并推导出了完全离散方案的误差估计。最后，提供了一些数值实验来验证理论结果并说明所提出方案的准确性和效率。