In this article we study a well-posedness and finite element approximation for the non-isothermal incompressible magneto-hydrodynamics flow subject to a generalized Boussinesq problem with temperature-dependent parameters. Applying some similar hypotheses in Oyarźua et al. (IMA J Numer Anal 34:1104–1135, 2014), we prove the existence and uniqueness of weak solutions and discrete weak solutions, and derive optimal error estimates for small and smooth solutions. Finally, we provide some numerical results to confirm the rates of convergence.

中文翻译：

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具有温度相关参数的平稳磁流体动力学问题的适定性和有限元逼近

在本文中，我们研究了具有温度依赖参数的广义Boussinesq问题的非等温不可压缩磁流体动力学流动的适定性和有限元逼近。在Oyarźua等人中应用一些类似的假设。（IMA J Numer Anal 34：1104-1135，2014），我们证明了弱解和离散弱解的存在性和唯一性，并推导了小而平滑解的最优误差估计。最后，我们提供一些数值结果以确认收敛速度。