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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
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WRAP-analysis-patch-test-atomistic-coupling-finite-elements-Dedner-2017.pdf - Accepted Version - Requires a PDF viewer. Download (1062Kb) | Preview |
Official URL: https://doi.org/10.1051/m2an/2017013
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 | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of 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: |
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| 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 | |||||||||
| Funder: | University of Warwick Mathematics and Statistics Doctoral Training Centre (MASDOC) | |||||||||
| RIOXX Funder/Project Grant: |
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