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Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces : a two-dimensional model problem
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Ortner, Christoph and Zhang, L. (2012) Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces : a two-dimensional model problem. SIAM Journal on Numerical Analysis, Volume 50 (Number 6). pp. 2940-2965. doi:10.1137/110851791 ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/110851791
Abstract
We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For many-body nearest-neighbor interactions on the two-dimensional triangular lattice, we show that patch test consistent a/c methods can be constructed for arbitrary interface geometries. Moreover, we prove that all methods within this class are first-order consistent at the atomistic/continuum interface and second-order consistent in the interior of the continuum region.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Multiscale modeling, Continuum mechanics | ||||||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||
ISSN: | 0036-1429 | ||||||||
Official Date: | 6 November 2012 | ||||||||
Dates: |
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Volume: | Volume 50 | ||||||||
Number: | Number 6 | ||||||||
Page Range: | pp. 2940-2965 | ||||||||
DOI: | 10.1137/110851791 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 27 December 2015 | ||||||||
Date of first compliant Open Access: | 27 December 2015 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
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