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Analysis of blended atomistic/continuum hybrid methods

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Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z ISSN 0029-599X.

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Official URL: http://doi.org/10.1007/s00211-015-0772-z

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Abstract

We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for finite range many-body interactions (e.g., EAM type), and in the presence of lattice defects (we consider point defects and dislocations). The two key ingredients in the analysis are (1) new force and energy consistency error estimates; and (2) a new technique for proving energy norm stability of a/c couplings that requires only the assumption that the exact atomistic solution is a stable equilibrium.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QP Physiology
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Molecular dynamics, Continuum mechanics
Journal or Publication Title: Numerische Mathematik
Publisher: Springer
ISSN: 0029-599X
Official Date: October 2016
Dates:
DateEvent
October 2016Published
19 November 2015Available
5 September 2015Accepted
Volume: 134
Number: 2
Page Range: pp. 275-326
DOI: 10.1007/s00211-015-0772-z
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 2 March 2017
Date of first compliant Open Access: 2 March 2017
Funder: Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC), Leverhulme Trust (LT), United States. Air Force. Office of Scientific Research (AFOSR)
Grant number: EP/H003096 (EPSRC), Starting Grant 335120 (ERC)

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