报告题目：Finite element methods for thermally driven incompressible Magnetohydrodynamic problems
报 告 人：毛士鹏 研究员 中国科学院数学与系统科学研究院
报告时间：2020年8月13日 15:00-16:00
报告地点：腾讯会议 ID：146 344 477
会议链接：https://meeting.tencent.com/s/4bvY3hP9K5AW
校内联系人：陶詹晶 zjtao@jlu.edu.cn
报告摘要：
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.
报告人简介：
毛士鹏，中国科学院数学与系统科学研究院研究员、博士生导师。2008年获中国科学院数学与系统科学研究院理学博士学位,然后留所工作至今，期间于2008-2012年分别在法国的INRIA以及在瑞士苏黎世联邦理工学院(ETH Zurich) 做博士后和研究助理。主要研究工作包括各向异性有限元，自适应有限元，非标准有限元方法以及磁流体力学计算等方面，至今已发表论文60余篇，曾入选中科院青年创新促进会会员和获得中科院朱李月华优秀教师奖。
