Volume 27, Issue 1
A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

Mingjie Liao, Ping Lin & Lei Zhang

Commun. Comput. Phys., 27 (2020), pp. 198-226.

Published online: 2019-10

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  • Abstract

In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is quasi-optimal if the continuum model is discretized by P1 finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.

  • Keywords

Atomistic models, coarse graining, atomistic-to-continuum coupling, quasicontinuum method, a posteriori error estimate.

  • AMS Subject Headings

65N12, 65N15, 70C20, 82D25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mliao@xs.ustb.edu.cn (Mingjie Liao)

plin@maths.dundee.ac.uk (Ping Lin)

lzhang2012@sjtu.edu.cn (Lei Zhang)

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