Please use this identifier to cite or link to this item: https://doi.org/10.1137/050636772
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dc.titleConvergence analysis of a quasi-continuum approximation for a two-dimensional material without defects
dc.contributor.authorLin, P.
dc.date.accessioned2014-10-28T02:32:55Z
dc.date.available2014-10-28T02:32:55Z
dc.date.issued2007
dc.identifier.citationLin, 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
dc.identifier.issn00361429
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103064
dc.description.abstractIn 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.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1137/050636772
dc.sourceScopus
dc.subjectFinite element method
dc.subjectGlobal minimization
dc.subjectLattice statics
dc.subjectLennard-Jones potential
dc.subjectMaterial defects
dc.subjectQuasi-continuum approximation
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1137/050636772
dc.description.sourcetitleSIAM Journal on Numerical Analysis
dc.description.volume45
dc.description.issue1
dc.description.page313-332
dc.description.codenSJNAA
dc.identifier.isiut000244631600016
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