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三元名家论坛-A constrained transport divergence-free finite element method for incompressible MHD equations
作者:     日期:2022-06-10     来源:     阅读:

讲座主题:A constrained transport divergence-free finite element method for incompressible MHD equations

专家姓名:郑伟英

工作单位:中国科学院数学与系统科学研究院

讲座时间:2022年6月13日 15:00-16:30

讲座地点:腾讯会议:168 518 977

主办单位:yabo亚博国际数学与信息科学学院

内容摘要:

We study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method, we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom. A comparison with other discretization using lid driven cavity is also given.

主讲人介绍:

郑伟英,中国科学院数学与系统科学研究院研究员,主要从事有限元方法的理论与应用研究,包括电磁和流体计算等,在Maxwell方程自适应多重网格方法的最优收敛性、分层介质散射问题以及三维磁流体计算等方面取得重要研究进展。2017年获国家杰出青年科学基金资助,2019年任中科院数学与系统科学研究院“冯康首席研究员”,2021年获冯康科学计算奖。