In this paper, we consider a first-order projection finite element scheme for the three dimensional incompressible magnetohydrodynamics system based on a magnetic vector potential formulation by writing the magnetic induction , where is a magnetic potential. The main advantage of this projection scheme has two-fold. One is that numerical solutions of velocity field and magnetic induction both satisfy the divergence-free condition in fully discrete level. Another is that the proposed scheme is unconditionally stable for any mesh size and time step size. Under a reasonable regularity assumption, we derive spatial–temporal error estimates of the velocity and magnetic vector potential. Finally, numerical results are displayed to illustrate convergence rates.

中文翻译：

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不可压缩矢量势磁流体动力学系统一阶无条件稳定投影有限元法


在本文中，我们考虑了基于磁矢量势公式的三维不可压缩磁流体动力学系统的一阶投影有限元格式，通过写出磁感应强度 ，其中 是磁势。这种投影方案的主要优点有两个。一是速度场和磁感应强度的数值解均满足全离散水平的无散度条件。另一个是所提出的方案对于任何网格大小和时间步长都是无条件稳定的。在合理的规律性假设下，我们得出速度和磁矢量势的时空误差估计。最后，显示数值结果来说明收敛速度。