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Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice
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Ortner, Christoph and Shapeev, A. V. (2013) Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice. Mathematics of Computation, Volume 82 (Number 284). pp. 2191-2236. doi:10.1090/S0025-5718-2013-02687-7 ISSN 0025-5718.
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Official URL: http://dx.doi.org/10.1090/S0025-5718-2013-02687-7
Abstract
We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3):905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy defects.
We establish first-order consistency and stability of the method, from which we obtain a priori error estimates in the H1-norm and the energy in terms of the mesh size and the "smoothness'' of the atomistic solution in the continuum region. From these error estimates we obtain heuristics for an optimal choice of the atomistic region and the finite element mesh, as well as convergence rates in terms of the number of degrees of freedom. Our analytical predictions are supported by extensive numerical tests.
| 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, Crystalline polymers -- Defects -- Mathematical models, Error analysis (Mathematics) | ||||
| Journal or Publication Title: | Mathematics of Computation | ||||
| Publisher: | American Mathematical Society | ||||
| ISSN: | 0025-5718 | ||||
| Official Date: | 22 April 2013 | ||||
| Dates: |
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| Volume: | Volume 82 | ||||
| Number: | Number 284 | ||||
| Page Range: | pp. 2191-2236 | ||||
| DOI: | 10.1090/S0025-5718-2013-02687-7 | ||||
| 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) |
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