Error estimate of a finite element method using stress intensity factor

被引：4

作者：

Cai, Zhiqiang ^{[1
]}

Kim, Seokchan ^{[2
]}

Lee, Hyung-Chun ^{[3
]}

机构：

[1] Purdue Univ, Dept Math, 150 Univ St, W Lafayette, IN 47907 USA

[2] Changwon Natl Univ, Dept Math, Chang Won, South Korea

[3] Ajou Univ, Dept Math, Suwon, South Korea

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 76卷 / 10期

基金：

美国国家科学基金会; 新加坡国家研究基金会;

关键词：

Finite element; Corner singularity; Singular function; Stress intensity factor; SINGULAR FUNCTIONS; CORNER SINGULARITIES; POISSON EQUATION; DOMAINS;

D O I：

10.1016/j.camwa.2018.08.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algorithm on computing accurate finite element approximation to the Poisson equation on a polygonal domain with corner singularities was studied in Kim and Lee (2016, 2017) numerically. The algorithm requires several iterations depending on singularities of the solution. Each iteration requires a solution of the standard finite element approximation to the Poisson equation with possible different Dirichlet data and the corresponding stress intensity factors. This paper provides an error estimate of the finite element approximation given by the algorithm, and, hence, determine the number of iterations needed to achieve full rates of convergence in both the energy and the L-2 norms. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：2402 / 2408

页数：7

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