Please use this identifier to cite or link to this item: https://doi.org/10.1137/050636772
Title: Convergence analysis of a quasi-continuum approximation for a two-dimensional material without defects
Authors: Lin, P. 
Keywords: Finite element method
Global minimization
Lattice statics
Lennard-Jones potential
Material defects
Quasi-continuum approximation
Issue Date: 2007
Citation: Lin, P. (2007). Convergence analysis of a quasi-continuum approximation for a two-dimensional material without defects. SIAM Journal on Numerical Analysis 45 (1) : 313-332. ScholarBank@NUS Repository. https://doi.org/10.1137/050636772
Abstract: In many applications, materials are modeled by a large number of particles (or atoms), where any particle can interact with any other. The computational cost is very high since the number of atoms is huge. Recently much attention has been paid to a so-called quasi-continuum (QC) method, which is a mixed atomistic/continuum model. The QC method uses an adaptive finite element framework to effectively integrate the majority of the atomistic degrees of freedom in regions where there is no serious defect. However, numerical analysis of this method is still in its infancy. In this paper we will conduct a convergence analysis of the QC method in the case when there is no defect. We will also remark on the case when the defect region is small. The difference between our analysis and conventional analysis is that our exact atomistic solution is not a solution of a continuous partial differential equation, but a discrete lattice scale solution which is not approximately related to any conventional partial differential equation. © 2007 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Numerical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/103064
ISSN: 00361429
DOI: 10.1137/050636772
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