報告題目：Finite element methods for thermally driven incompressible Magnetohydrodynamic problems
報 告 人：毛士鵬 研究員 中國科學院數學與系統科學研究院
報告時間：2020年8月13日 15:00-16:00
報告地點：騰訊會議 ID：146 344 477
會議鍊接：https://meeting.tencent.com/s/4bvY3hP9K5AW
校内聯系人：陶詹晶 zjtao@jlu.edu.cn
報告摘要：
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. To overcome the difficulties of very low regularity of the heat source terms, 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 Nedelec 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.
報告人簡介：
毛士鵬，中國科學院數學與系統科學研究院研究員、博士生導師。2008年獲中國科學院數學與系統科學研究院理學博士學位,然後留所工作至今，期間于2008-2012年分别在法國的INRIA以及在瑞士蘇黎世聯邦理工學院(ETH Zurich) 做博士後和研究助理。主要研究工作包括各向異性有限元，自适應有限元，非标準有限元方法以及磁流體力學計算等方面，至今已發表論文60餘篇，曾入選中科院青年創新促進會會員和獲得中科院朱李月華優秀教師獎。
