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学术报告-毛士鹏

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2020-12-07 08:51:03

学术报告


题      目: Convergence analysis of finite element method for natural convection MHD

报  告  人:毛士鹏   研究员  (邀请人:钟柳强 )

                                   中国科学院数学与系统科学研究院



时      间:2020-12-07 15:00--16:00


地      点:学院502


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,中国科学院大学岗位教授。2008年获中国科学院博士学位,先后在法国Université de Pau ,Université de Valencienne,INRIA,和瑞士苏黎世联邦理工(ETHZ)访问交流与博士后研究。主要研究方向为有限元方法及其应用以及磁流体力学计算等。在 Numer. Math.、Math. Comp., SIAM. J. Numer. Math., SIAM J.Sci.C omputing,M3AS等杂志上发表论文50余篇。曾经获得EASIAM论文竞赛一等奖,中国计算数学学会优秀青年论文一等奖,中国科学院院长奖等诸多荣誉称。

摘      要:

       We propose and study a numerical scheme for the time-dependent magnetohydrodynamic problem with low magnetic Reynolds number coupled heat equation through the well-known Boussinesq approximation, in which the Joule effect and Viscous heaing are taken into account. We first show the uniqueness of solution for the continuous model under some regularity assumptions on the weak solution. Then a fully discrete Euler semi- implicit scheme based on the mixed finite element method for the model is developed, in which continuous elements are used to approximate the fluid equations, thermally equation and electric potential poisson equation. The proposed discrete scheme requires only solving a linear system per time step. With a proper regularity assumption on the exact solution, the unconditionally optimal convergence in H1-norm of the fully discrete finite element solution for each unknown variable without any restriction on the time-step size is derived. Finally, several numerical examples are performed to demonstrate both accuracy and efficiency of our proposed scheme.