no. 6
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.

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
Mots clés : 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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     author = {Dedner, Andreas and Ortner, Chistoph and Wu, Huan},
     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},
     volume = {51},
     number = {6},
     year = {2017},
     doi = {10.1051/m2an/2017013},
     zbl = {1383.82062},
     mrnumber = {3745172},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2017013/}
}
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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. http://www.numdam.org/articles/10.1051/m2an/2017013/

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