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
收藏
页码：1889 / 1922
页数：34
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