题目：Spectral-Correct and Spurious-Free New Mixed Elements for Maxwell Eigenvalue Problem

报告人：段火元 教授 （武汉大学）

地点：致远楼101室

时间：2019年3月29日 星期三 上午10:00-11:00

报告摘要：

New inf-sup stable mixed elements are proposed and analyzed for solving the Maxwell equations in terms of electric field and Lagrange multiplier. Nodal- continuous Lagrange elements of any order on simplexes in two- and three- dimensional spaces can be used for the electric field. The multiplier is compatibly approximated always by the discontinuous piecewise constant elements. A general theory of stability and error estimates is developed; when applied to the eigenvalue problem, by establishing the key property of discrete compactness, we show that the proposed mixed elements provide spectral-correct, spurious-free approximations. Essentially optimal error bounds (only up to an arbitrarily small constant) are obtained for eigenvalues and for both singular and smooth eigenfunction solutions. Numerical experiments are performed for Maxwell eigenvalue problem in nonsmooth domains to illustrate the theoretical results.

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。研究兴趣包括如下一些：偏微分方程及特征值问题数值解，有限元方法及其理论分析，多重网格算法，自适应算法，预处理迭代算法，PDE 最优控制问题数值方法，反问题数值方法，等等；研究的问题包括如下一些：Maxwell equations，Navier-Stokes equations, convection-diffusion-reaction equation, Reissner- Mindlin plate problem, shell problem, elasticity problem, MHD equations (magnetohydrodynamic equations)，等等。在国内外学术期刊发表论文50多篇，包括SIAM Journal on Numerical Analysis，Mathematics of Computation，Numerische Mathematik，Computer Methods in Applied Mechanics and Engineering，IMA Journal of Numerical Analysis，Journal of Computational Physics, SIAM Journal on Scientific Computing等期刊。

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