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A priori error estimates for energy-based quasicontinuum approximations of a periodic chain
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Ortner, Christoph and Wang, Hao (2011) A priori error estimates for energy-based quasicontinuum approximations of a periodic chain. Mathematical Models and Methods in Applied Sciences, Volume 21 (Number 12). pp. 2491-2521. doi:10.1142/S0218202511005817 ISSN 0218-2025.
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Official URL: http://dx.doi.org/10.1142/S0218202511005817
Abstract
We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasi-nonlocal QC method.
Our analysis decomposes the consistency error into modeling and coarsening errors. While previous results on estimating the modeling error exist, we present a new and simpler proof based on negative-norm estimates. Our stability analysis extends previous results on sharp stability estimates under homogeneous strain to the nonlinear setting. Finally, we present numerical experiments to illustrate the results of our analysis.
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, Materials science, Continuum mechanics | ||||||
Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||
ISSN: | 0218-2025 | ||||||
Official Date: | 2011 | ||||||
Dates: |
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Volume: | Volume 21 | ||||||
Number: | Number 12 | ||||||
Page Range: | pp. 2491-2521 | ||||||
DOI: | 10.1142/S0218202511005817 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 20 December 2015 | ||||||
Date of first compliant Open Access: | 20 December 2015 | ||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC), University of Oxford |
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