题目： Finite element methods for thermally driven Magnetohydrodynamic problems including Joule heating

报告人：毛士鹏 教授

（中国科学院数学与系统科学研究院）

Abstract :  We study numerical methods for  the time-dependent magnetohydrodynamic coupled heat equation through the well-known Boussinesq approximation, in which the Joule effect and Viscous heating are taken into account. In view that the heat sources only belong to L^1(/Omega), a regularized weak system is proposed to deal with Joule and Viscous heating terms.  We  consider an Euler semi-implicit  semi-discrete scheme  for the regularized system.  As both discrete parameter and regularization parameter tend to zero, we prove that the discrete solution converges to a weak solution of the original problem.  Furthermore, we establish  the uniqueness of the weak solution provided it satisfies a smoother condition.  Next, we consider the fully discrete Euler semi-implicit scheme based on  the mixed finite method to approximate the  fluid  equation and N$/mathrm{/acute{e}}$d$/mathrm{/acute{e}}$lec edge element to  the magnetic induction. The fully discrete scheme requires only solving a linear system per time step.   The error estimates for  the velocity, magnetic induction and temperature are derived under  a proper regularity  assumption for the exact solution. Finally, several numerical examples are performed to demonstrate  both accuracy and efficiency of our proposed scheme.

时间：2019年7月1日（周一)

晚上19:30-20:30

地点：565net必赢客户端本部教二楼627教室

联系人：赵旭鹰

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