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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

DOI: 10.4208/cicp.OA-2018-0169

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)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-198, author = {Liao , MingjieLin , Ping and Zhang , Lei}, title = {A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {1}, pages = {198--226}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0169}, url = {http://global-sci.org/intro/article_detail/cicp/13319.html} }
TY - JOUR T1 - A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions AU - Liao , Mingjie AU - Lin , Ping AU - Zhang , Lei JO - Communications in Computational Physics VL - 1 SP - 198 EP - 226 PY - 2019 DA - 2019/10 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0169 UR - https://global-sci.org/intro/article_detail/cicp/13319.html KW - Atomistic models, coarse graining, atomistic-to-continuum coupling, quasicontinuum method, a posteriori error estimate. AB -

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.

Mingjie Liao, Ping Lin & Lei Zhang. (2019). A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions. Communications in Computational Physics. 27 (1). 198-226. doi:10.4208/cicp.OA-2018-0169
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