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科学研究
RESEARCH
An adaptive finite element method for cathodic protection
时间  Datetime
2021-01-04 10:30 — 11:30
地点  Venue
教室(630)
报告人  Speaker
徐一峰
单位  Affiliation
上海师范大学数理学院
邀请人  Host
黄建国
备注  remarks
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 Prof. Guanglian Li at The University of Hong Kong.