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

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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
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
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:	Date Event 6 October 2013 Available 23 June 2012 Submitted
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
Funder:	Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC), University of Oxford, Sichuan da xue [Sichuan University]

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