Geodesic
Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements
Dedner, Andreas1  ; Ortner, Chistoph1 ; Wu, Huan1
1 Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2263-2288

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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.

DOI : 10.1051/m2an/2017013
Classification : 65N12, 65N15, 70C20
Keywords: Atomistic models, coarse graining, atomistic-to-continuum coupling, quasicontinuum method, error analysis

Dedner, Andreas 1 ; Ortner, Chistoph 1 ; Wu, Huan 1

1 Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK. 
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     title = {Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2263--2288},
     publisher = {EDP-Sciences},
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Dedner, Andreas; Ortner, Chistoph; Wu, Huan. Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2263-2288. doi: 10.1051/m2an/2017013

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