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A posteriori error control for a quasi-continuum approximation of a periodic chain
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Ortner, Christoph and Wang, Hoa (2013) A posteriori error control for a quasi-continuum approximation of a periodic chain. IMA Journal of Numerical Analysis, Volume 34 (Number 3). pp. 977-1001. doi:10.1093/imanum/drt011 ISSN 0272-4979.
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Official URL: http://dx.doi.org/10.1093/imanum/drt011
Abstract
We consider a one-dimensional periodic atomistic model, for which we formulate and analyse an adaptive variant of a quasicontinuum method. We establish a posteriori error estimators for the energy norm and for the energy, based on a posteriori residual and stability estimates. We formulate adaptive mesh refinement algorithms based on these error estimators. Our numerical experiments indicate optimal convergence rates of these algorithms.
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, Error analysis (Mathematics) | ||||||
Journal or Publication Title: | IMA Journal of Numerical Analysis | ||||||
Publisher: | Oxford University Press | ||||||
ISSN: | 0272-4979 | ||||||
Official Date: | 6 October 2013 | ||||||
Dates: |
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Volume: | Volume 34 | ||||||
Number: | Number 3 | ||||||
Page Range: | pp. 977-1001 | ||||||
DOI: | 10.1093/imanum/drt011 | ||||||
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), China Scholarship Council (CSC), University of Oxford, Sichuan da xue [Sichuan University] |
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