北京科学与工程计算研究院学术报告之七十四

报告人/Speaker: 徐一峰(上海师范大学)


报告题目/Title: An adaptive finite element method for cathodic protection


时间/Date & Time: Aug. 16, 2018


地点/Location: 理科楼M843,BISEC


报告摘要/Abstract:
In this talk, I shall introduce an adaptive finite element method for numerical approximations of a cathodic protection problem, which is governed by a steady-state diffusion equation with a nonlinear boundary condition. The algorithm is first shown to guarantee strong convergence of discrete solutions to the exact solution and a vanishing limit of relevant estimators. Then it is proved to be contractive for a sum of the energy error and the scaled estimator after each refinement step. This ensures a quasi-optimal convergence rate in terms of the number of elements over underlying triangulations. Two numerical examples are also presented to illustrate the optimal convergence and efficiency of the adaptive algorithm. This is a joint work with Guanglian Li at Imperial College London, UK.


报告人简介/About the speaker:
徐一峰,上海师范大学副教授。2007年于香港中文大学获得数学博士学位,2008年至2010年于上海交通大学做博士后研究。香港中文大学、美国加州大学尔湾分校、伦敦大学学院、香港浸会大学、美国北卡罗来纳大学夏洛特分校访问学者。研究兴趣为Finite element analysis, adaptive finite element methods including mixed, discontinuous Galerkin and   nonconforming methods, and applications in elasticity, electromagnetism and inverse problems等。在IMA Journal of Numerical Analysis、ESAIM: Mathematical Modeling and Numerical Analysis、Journal of Computational Mathematics等刊物上发表论文十余篇。