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学术报告
学术报告
武汉大学数学与统计学院段火元教授报告通知(第ZJ2014034号)
发布人:系统管理员  威尼斯官方网站:2014-11-11   浏览次数:846

  应数学系张达治博士邀请,武汉大学数学与统计学院段火元教授将于近期访问我校并做报告,报告信息如下,欢迎感兴趣的老师和同学参加。

报告题目:Approximation of non H1 space very weak solution of Maxwell equations by H1-conforming nodal-continuous FEM

地点:格物楼503

时间:20141112日下午 1400

 

报告摘要:

In general, the solution of Maxwell equations may be singular and belongs to a non H1 space, i.e., a fractional-order Hr space for some real number r<1. The typical reason is due to the domain boundary which may carry reentrant corners and edges. Although nodal-continuous FEM has been long popular for computational fluid dynamics, it had never been really successful for the computation of Maxwell equations whenever the solution is outside H1 space. In fact, a wrong convergence phenomenon of the resultant H1-conforming nodal-continuous finite element solution has been widely known in both mathematical and engineering communities. Until the year 2002, a first method---weighted regularization method appeared which gives a correctly convergent H1-conforming nodal-continuous finite element solution. Since then, several methods have been developed which can also produce correct approximations from the H1-conforming nodal-continuous finite element space, even if the exact solution does not belong to the H1 space. In this lecture, I will give a review of the existing H1-conforming nodal-continuous FEMs and provide a number of numerical experiments for illustrating the performance of the L2-projection method in seeking correctly convergent H1-conforming nodal-continuous finite element solutions for Maxwell equations. Source problem and eigenproblem are considered.

 

报告人简介:

        段火元,武汉大学数学与统计学院教授,博士生导师,威尼斯官方网站登录数学系知名系友。研究方向:有限元方法、多重网格算法、自适应算法、预处理迭代算法、偏微分方程数值解;随机微分方程的数值方法及应用;图像处理的数值方法。在国内外学术期刊发表学术论文近50篇,包括国际著名期刊如SIAM Journal On Numerical AnalysisMathematics of ComputationNumerischeMathematikComputer Methods in Applied Mechanics and EngineeringJournal of Computational Physics等。

 

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