题目：Adaptive Finite Elements VIA Duality

报告人：章顺 博士 （香港城市大学）

时间：2023年10月19日 上午10：00-11：00

地点：致远楼101室

摘要：In this talk, we discuss two kinds of dualities and their applications in adaptive finite element methods.

The first duality is the duality from the convex optimization. Some PDE model has a natural energy to minimize.A complementary  energy maximization problem can also be derived. The duality gap between two energies provides an upper bound for the approximation error. We will discuss its applications in adaptive finite elements and reduced basis methods.

The second duality is the duality for the quantity of interest. By solving the primal and adjoint problems, a sharp error estimate can be derived for the error of the quantity of interest. We will discuss how to establish this kind of error estimate for the least-squares finite element method.

报告人简介：

Dr. Zhang got his Bachelor and Master's degrees in mathematics from Tongji University. After that, he got his PhD degree from Purdue University, USA. He did his postdoc at Division of Applied Mathematics, Brown University. Then, he moved to Hong Kong. Currently, he is an associate Professor at Department of Mathematics, City University of Hong Kong. He has published papers in top numerical analysis journals such as SIAM J. Numer Anal, SIAM J. Sci. Compt, Math. Comp., and Numer Math.

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