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  4. Analysis Of An Energy-Based Atomistic/Continuum Approximation Of A Vacancy In The 2D Triangular Lattice
 
research article

Analysis Of An Energy-Based Atomistic/Continuum Approximation Of A Vacancy In The 2D Triangular Lattice

Ortner, C.
•
Shapeev, A. V.
2013
Mathematics Of Computation

We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3): 905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy defects. We establish first-order consistency and stability of the method, from which we obtain a priori error estimates in the H-1-norm and the energy in terms of the mesh size and the "smoothness" of the atomistic solution in the continuum region. From these error estimates we obtain heuristics for an optimal choice of the atomistic region and the finite element mesh, as well as convergence rates in terms of the number of degrees of freedom. Our analytical predictions are supported by extensive numerical tests.

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Type
research article
DOI
10.1090/S0025-5718-2013-02687-7
Web of Science ID

WOS:000326291500013

Author(s)
Ortner, C.
Shapeev, A. V.
Date Issued

2013

Publisher

Amer Mathematical Soc

Published in
Mathematics Of Computation
Volume

82

Issue

284

Start page

2191

End page

2236

Subjects

Atomistic models

•

atomistic-to-continuum coupling

•

coarse graining

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
MATHICSE  
Available on Infoscience
December 9, 2013
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/97748
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