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：2014年11月12日下午 14：00

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.