A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain

被引：2
|
作者：
Wang, Hao [1 ]
Liu, Shaohui [2 ]
Yang, Feng [3 ]
机构：
[1] Sichuan Univ, Sch Math, 24 South Sect One, Chengdu 610065, Sichuan, Peoples R China
[2] SUNY Stony Brook, Dept Appl Math & Stat, Stony Brook, NY 11794 USA
[3] Beijing Univ, Coll Math Sci, Zhongguancun Rd 1, Beijing 100000, Peoples R China
来源：
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2019年 / 12卷 / 01期
关键词：
Atomistic-to-continuum coupling; a posteriori error estimate; adaptivity; force based method; FRENKEL-KONTOROVA MODEL; 2-BODY POTENTIALS; PERIODIC CHAIN; APPROXIMATION; CONVERGENCE; SIMULATIONS; OSCILLATION; DIMENSIONS; ADAPTIVITY; DEFECTS;
D O I：
10.4208/nmtma.OA-2017-0094
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the problem of a posteriori error estimates and adaptivity for three typical force-based atomistic-to-continuum coupling methods. Combining the residual and the stability estimates, we derive computable a posteriori error estimators for the three methods in the energy norm and formulate adaptive algorithms using these estimators. Our numerical experiments show optimal convergence rates of these algorithms. The efficiency of the estimators are also demonstrated numerically.
引用
收藏
页码：233 / 264
页数：32
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