A Convergent Adaptive Finite Element Method for Cathodic Protection

被引：1

作者：

Li, Guanglian ^{[1
]}

Xu, Yifeng ^{[2
,3
]}

机构：

[1] Univ Bonn, Inst Numer Simulat, Wegelerstr 6, D-53115 Bonn, Germany

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Shanghai Normal Univ, Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China

来源：

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2017年 / 17卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Cathodic Protection; Nonlinear Boundary Condition; A Posteriori Error Estimate; Adaptive Finite Element Method; Convergence; P-LAPLACIAN EQUATION;

D O I：

10.1515/cmam-2016-0032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we propose and analyze an adaptive finite element method for a steady-state diffusion equation with a nonlinear boundary condition arising in cathodic protection. Under a general assumption on the marking strategy, we show that the algorithm generates a sequence of discrete solutions that converges strongly to the exact solution in H-1(Omega) and the sequence of error estimators has a vanishing limit. Numerical results show clearly the convergence and efficiency of the adaptive algorithm.

引用

页码：105 / 120

页数：16

共 21 条

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