In this paper, we study a first-order Euler semi-implicit finite element scheme for the two-dimensional incompressible Boussinesq equations for magnetohydrodynamics convection with the temperature-dependent viscosity, electrical conductivity and thermal diffusivity. In finite element discretizations, the mini finite element is used to approximate the velocity and pressure, and the piecewise linear finite element is used to approximate the magnetic field and temperature. The unconditional stability of the proposed scheme is proved. By introducing three projection operators with variable coefficients and using the method of mathematical induction, we obtain optimal error estimates under a CFL type condition. Finally, numerical examples are provided to demonstrate these convergence rates.

中文翻译：

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二维不可压缩温度相关 MHD-Boussinesq 方程的线性化欧拉有限元格式的最优收敛分析


在本文中，我们研究了具有与温度相关的粘度、电导率和热扩散率的磁流体动力学对流二维不可压缩 Boussinesq 方程的一阶欧拉半隐式有限元格式。在有限元离散化中，使用迷你有限元来近似速度和压力，使用分段线性有限元来近似磁场和温度。证明了所提出方案的无条件稳定性。通过引入三个变系数投影算子并利用数学归纳法，我们获得了CFL型条件下的最优误差估计。最后，提供数值示例来证明这些收敛速度。