In this paper, we study and analyze a semi-discrete projection scheme for solving a hybrid magnetohydrodynamics equations coupled by the nonstationary Navier–Stokes equations and the stationary Maxwell equations. The suggested projection scheme is energy preserving and satisfies the divergence free condition of the velocity field at the discrete level. As the time step size is sufficiently small, we establish optimal temporal error estimates under some regularity assumptions. Numerical results are provided to show the efficiency of the suggested scheme and verify the theoretical analysis.

中文翻译：

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耦合磁流体动力学方程的节能投影方法的时间收敛分析

在本文中，我们研究和分析半离散投影方案，以求解由非平稳Navier–Stokes方程和平稳Maxwell方程耦合的混合磁流体动力学方程。建议的投影方案是节能的，并且在离散水平上满足速度场的无散度条件。由于时间步长足够小，我们在某些规律性假设下建立了最佳的时间误差估计。数值结果表明了该方案的有效性并验证了理论分析。