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Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements

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Dedner, Andreas, Ortner, Christoph and Wu, H. (2017) Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. ESAIM: Mathematical Modelling and Numerical Analysis, 51 (6). pp. 2263-2288. doi:10.1051/m2an/2017013 ISSN 0764-583X.

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Official URL: https://doi.org/10.1051/m2an/2017013

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Abstract

We formulate a patch test consistent atomistic-to-continuum coupling (a/c) scheme that employs a second-order (potentially higher-order) finite element method in the material bulk. We prove a sharp error estimate in the energy-norm, which demonstrates that this scheme is (quasi-)optimal amongst energy-based sharp-interface a/c schemes that employ the Cauchy–Born continuum model. Our analysis also shows that employing a higher-order continuum discretisation does not yield qualitative improvements to the rate of convergence.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Error analysis (Mathematics), Finite element method
Journal or Publication Title: ESAIM: Mathematical Modelling and Numerical Analysis
Publisher: EDP Sciences
ISSN: 0764-583X
Official Date: 12 November 2017
Dates:
DateEvent
12 November 2017Published
16 March 2017Accepted
Volume: 51
Number: 6
Page Range: pp. 2263-2288
DOI: 10.1051/m2an/2017013
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 5 April 2017
Date of first compliant Open Access: 23 April 2018
Funder: University of Warwick Mathematics and Statistics Doctoral Training Centre (MASDOC)
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/H023364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
35120H2020 European Research Councilhttp://dx.doi.org/10.13039/100010663
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