We revise the structure-preserving finite element method in [K. Hu, Y. MA and J. Xu. (2017) Stable finite element methods preserving $\nabla \cdot \mathbf{B}=0$ exactly for MHD models. Numer. Math., 135, 371-396]. The revised method is semi-implicit in time-discretization. We prove the linearized scheme preserves the divergence free property for the magnetic field exactly at each time step. Further, we showed the linearized scheme is unconditionally stable and we obtain optimal convergence in the energy norm of the revised method even for solutions with low regularity.

中文翻译：

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非平稳不可压缩磁流体动力学方程的半隐式保结构有限元分析

我们在[K. 胡永马和徐建 （2017）保留稳定的有限元方法$\nabla \cdot \mathbf{乙}=0$完全适用于MHD型号。努默。数学，135，371-396]。修改后的方法在时间离散上是半隐式的。我们证明了线性化方案精确地在每个时间步都保留了磁场的无散度特性。此外，我们证明了线性化方案是无条件稳定的，并且即使对于规则性较低的解，我们也能在修正方法的能量范数中获得最佳收敛。