A POSTERIORI ERROR ANALYSIS OF FINITE ELEMENT METHOD FOR LINEAR NONLOCAL DIFFUSION AND PERIDYNAMIC MODELS

被引：62

作者：

Du, Qiang ^{[1
]}

Ju, Lili ^{[2
]}

Tian, Li ^{[1
]}

Zhou, Kun ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

来源：

MATHEMATICS OF COMPUTATION | 2013年 / 82卷 / 284期

基金：

美国国家科学基金会;

关键词：

Peridynamic models; nonlocal diffusion; a posteriori error estimate; finite element; INTEGRAL-EQUATIONS; VECTOR CALCULUS; NAVIER EQUATION; CONVERGENCE;

D O I：

10.1090/S0025-5718-2013-02708-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present some results on a posteriori error analysis of finite element methods for solving linear nonlocal diffusion and bond-based peridynamic models. In particular, we aim to propose a general abstract frame work for a posteriori error analysis of the peridynamic problems. A posteriori error estimators are consequently prompted, the reliability and efficiency of the estimators are proved. Connections between nonlocal a posteriori error estimation and classical local estimation are studied within continuous finite element space. Numerical experiments (1D) are also given to test the theoretical conclusions.

引用

页码：1889 / 1922

页数：34

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