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：烟台大学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。