由哈尔滨工业大学国际合作部“国际学者云课堂”系列活动组织，应数学学院郭玉坤教授的邀请，美国密歇根理工大学数学系孙继广教授将于近日在我院做六场系列学术讲座。以下是报告信息，欢迎感兴趣的广大师生参加。

讲座时间：2022年5月23-25日，每日上午8:30-11:30

讲座平台：腾讯会议，会议号686-1468-0195

讲座题目：Regular Convergence and Finite Element Methods for Eigenvalue Problems

讲座摘要：In this series of lectures, we discuss regular convergence and its application to the analysis of finite element methods for eigenvalues problem. Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. Focusing on the finite element methods (conforming, non-conforming, discontinuous Galerkin, etc.) for eigenvalue problems, we show that the regular convergence depends on the approximation property of the finite element spaces and the point convergence of the discrete solution operators. Combining the discrete approximation theory for the eigenvalue problems of holomorphic Fredholm operators, the result can be used to show the convergence of many finite element methods for eigenvalue problems of elliptic partial differential equations, e.g., the Dirichlet eigenvalue problem.

The main topics are listed below.

1. Finite element methods for eigenvalue problems of partial different equations.

2. Regular convergence and other types of discrete convergence; discrete convergence of eigenvalue problems of holomorphic Fredholm operator functions

3. Dirichlet eigenvalue problem - conforming methods and non-conforming methods, discontinuous Galerkin methods

4. Biharmonic eigenvalue problem - conforming methods and non-conforming methods, discontinuous Galerkin methods

References

[1] G. Vainikko, Funktionalanalysis der Diskretisierungsmethoden. Teubner-Texte zur Mathematik. B. G. Teubner Verlag, Leipzig, 1976.

[2] J. Sun and A. Zhou, Finite element methods for eigenvalue problems. CRC Press, Taylor & Francis Group, Boca Raton, 2016.

主讲人简介：孙继广1996年毕业于清华大学应用数学系，2005年在University of Delaware获得应用数学博士。现在任Michigan Technological University终身正教授（tenured full professor）。孙继广的研究方向包括特征值问题有限元方法和逆散射理论：传输特征值的计算，非共轭矩阵特征值的围道积分方法，非线性特征值计算收敛性分析的解析算子函数方法，反散射问题的采样法，贝叶斯反问题以及穿墙探测问题。从2004年至今在Inverse Problems, SIAM Journal of Numerical Analysis, Numerische Mathematik, SIAM Journal on Imaging Sciences, SIAM Journal on Scientific Computing, Journal of Computational Physics等杂志上发表80余篇文章以及一部合作的专著Finite Element Methods for Eigenvalue Problems，Taylor & Francis，2016。