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A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D


Author: Christoph Ortner
Journal: Math. Comp. 80 (2011), 1265-1285
MSC (2010): Primary 65N12, 65N15, 70C20
DOI: https://doi.org/10.1090/S0025-5718-2010-02453-6
Published electronically: December 31, 2010
MathSciNet review: 2785458
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Abstract: For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially guarantee a one-to-one correspondence between atomistic solutions and QNL-QC solutions. The analysis is based on consistency error estimates in negative norms, novel a priori and a posteriori stability estimates, and a quantitative inverse function theorem.


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Additional Information

Christoph Ortner
Affiliation: Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, United Kingdom
Email: ortner@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-2010-02453-6
Keywords: Quasicontinuum method, quasinonlocal coupling, finite deformations, sharp stability, error analysis
Received by editor(s): November 7, 2009
Received by editor(s) in revised form: May 15, 2010
Published electronically: December 31, 2010
Additional Notes: This work was supported by the EPSRC Critical Mass Programme “New Frontiers in the Mathematics of Solids”.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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