| Issue |
ESAIM: M2AN
Volume 51, Number 6, November-December 2017
|
|
|---|---|---|
| Page(s) | 2263 - 2288 | |
| DOI | https://doi.org/10.1051/m2an/2017013 | |
| Published online | 12 December 2017 | |
Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements∗
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK.
a.s.dedner@warwick.ac.uk; c.ortner@warwick.ac.uk; huan.wu@warwick.ac.uk
Received: 24 October 2016
Revised: 15 March 2017
Accepted: 16 March 2017
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.
Mathematics Subject Classification: 65N12 / 65N15 / 70C20
Key words: Atomistic models / coarse graining / atomistic-to-continuum coupling / quasicontinuum method / error analysis
© EDP Sciences, SMAI 2017
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