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Analysis of Geometrically Consistent Schemes with Finite Range Interaction

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  31 October 2017

Hongliang Li  and
Pingbing Ming
Hongliang Li*
Affiliation:
Institute of Electronic Engineering, Microsystem and Terahertz Research Center, China Academy of Engineering Physics, Mianyang, 621900, China
Pingbing Ming*
Affiliation:
The State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, East Road Zhong-Guan-Cun, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
*
*Corresponding author. Email addresses:lihongliang@mtrc.ac.cn(H. L. Li), mpb@lsec.cc.ac.cn(P. B. Ming)
*Corresponding author. Email addresses:lihongliang@mtrc.ac.cn(H. L. Li), mpb@lsec.cc.ac.cn(P. B. Ming)
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Abstract

We analyze the geometrically consistent schemes proposed by E. Lu and Yang [6] for one-dimensional problem with finite range interaction. The existence of the reconstruction coefficients is proved, and optimal error estimate is derived under sharp stability condition. Numerical experiments are performed to confirm the theoretical results.

Keywords

Quasicontinuum methodatomic-to-continuum couplingstabilityfinite range interactions

MSC classification

Secondary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 5 , November 2017 , pp. 1333 - 1361
Copyright
Copyright © Global-Science Press 2017 

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