论文标题
分析非平稳性不可压缩磁性流体动力学方程的半图表呈现有限元法
Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations
论文作者
论文摘要
我们在[K。中修改了结构保存有限元方法Hu，Y. Ma和J. Xu。 （2017）稳定的有限元方法保留$ \ nabla \ cdot \ mathbf {b} = 0 $完全适用于MHD模型。 numer。 Math。，135，371-396]。修订后的方法是时间限制的半平等。我们证明，线性化方案在每个时间步骤中精确地保留了磁场的无分流特性。此外，我们显示线性化方案是无条件稳定的，即使对于较低的规律性溶液，我们也可以在修订方法的能量规范中获得最佳收敛。
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.
