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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
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by Christoph Ortner PDF
Math. Comp. 80 (2011), 1265-1285 Request permission

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
  • MR Author ID: 803698
  • Email: ortner@maths.ox.ac.uk
  • 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”.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1265-1285
  • MSC (2010): Primary 65N12, 65N15, 70C20
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02453-6
  • MathSciNet review: 2785458