In this article we consider a fully discrete Euler semi-implicit scheme for the nonstationary electromagnetically and thermally driven flow, which is describing the motion of a nonisothermal incompressible magneto-hydrodyna-mics fluid subject to generalized Boussinesq problem with temperature dependent parameters. A prototypical time-stepping scheme, which is comprised of the Euler semi-implicit discretization in time and conforming mixed finite element approximation in space is studied in detail. We obtain that the proposed scheme is unconditionally stable and derive some optimal error estimates for the fluid velocity, the fluid magnetic and the fluid temperature. Moreover, a suboptimal error estimate for the fluid pressure is proved. Numerical results are provided to verify the theoretical rates of the scheme.

在本文中，我们考虑用于非平稳电磁和热驱动流的​​完全离散Euler半隐式方案，该方案描述了具有温度依赖性参数的广义Boussinesq问题的非等温不可压缩磁流体动力学流体的运动。详细研究了一种典型的时间步长方案，该方案由时间的欧拉半隐式离散化和空间中的符合混合有限元逼近组成。我们发现，所提出的方案是无条件稳定的，并针对流体速度，流体磁和流体温度得出了一些最佳误差估计。此外，证明了对流体压力的次优误差估计。提供数值结果以验证该方案的理论速率。