报告人: 段火元 (武汉大学)
摘 要: As is well-known, there are many finite element methods for solving Maxwell equations, such as Nedelec element method, DG method, etc. In this talk, I will talk about the nodal-continuous Lagrange element for solving Maxwell equations. Usually, nodal-continuous elements have been widely used for computational fluid dynamics and solid mechanics, but not for computational electromagnetism. As a matter of fact, till 2002, have continuous elements been firstly really successfully applicable to Maxwell equations, from the paper in the well-renowned journal Numerische Mathematik by M. Costabel and M. Dauge. The main reason challenging issues are two. One is the singular solution which does not belong to $H1$ space. The other is the spurious eigenmodes. Since then, several methods gave been developed. Among others, I and co-authors have proposed a class of methods based on $L2$ projections, which allow the use if nodal-continuous elements. Theoretically and numerically, the methods can well approximate Maxwell equations, behaving like the Nedelec elements, no matter whether the solutions are singular or not, no matter whether the media homogeneous or inhomogeneous, no matter whether the source problem or the eigenvalue problem is solved.
报告人简介： 段火元，武汉大学数学与统计学院，教授，博导。2003-2009 新加坡国立大学、英国邓迪大学长期工作。2009年南开大学国外人才引进，南开大学数学科学学院，教授，博导。2013年起，武汉大学数学与统计学院教授。主要从事有限元方法研究，涉及多类偏微分方程数值解，例如 Maxwell 方程，Navier-Stokes 方程，对流扩散反应方程，板壳问题等。在国内外期刊发表学术论文五十余篇，包括计算数学领域的著名期刊：SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik, SIAM Journal on Scientific Computing, Journal of Computational Physics, IMA Journal of Numerical Analysis等。