报告题目：Conservative finite element method for incompressible MHD equations

报告人：郑伟英 研究员

报告时间：2019年10月11日（周五）8:30—10:00 

报告地点：威廉希尔学术报告厅

报告摘要：We propose a finite element method for the three-dimensional transient incompressible magneto hydrodynamic equations that ensures exactly divergence-free approximations of the velocity and the magnetic induction. We employ second-order semi-implicit time stepping, for which we rigorously establish an energy law and, as a consequence, unconditional stability. We prove unique solvability of the linear systems of equations to be solved in every time step. For those we design an efficient preconditioner so that the number of preconditioned GMRES iterations is uniformly bounded with respect to the number of degrees of freedom. As both mesh width and time step size tend to zero, we prove that the discrete solutions converge to a weak solution of the continuous problem. Finally, by several numerical experiments, we confirm the predictions of the theory and demonstrate the efficiency of the preconditioner.

个人简介：郑伟英，中国科学院数学与系统科学研究院研究员，国家杰出青年科学基金获得者，科学工程计算国家重点实验室副主任。1996年和1999年于郑州大学分别获学士、硕士学位，2002年于北京大学获博士学位，2006.11—2007.12为慕尼黑工业大学洪堡基金访问学者，2017年获国家杰出青年科学基金资助。现从事有限元方法的理论与应用研究，应用领域包括电磁场计算和磁流体力学计算等。在大型变压器的可计算建模、三维磁流体的高效数值方法和分层介质电磁散射等方向取得突破性成果，在SIAM系列杂志、Numer.Math.等计算数学核心杂志发表学术论文十余篇。

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2019年9月25日