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

Authors

  • Mingjie Liao School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P.R. China.
  • Ping Lin Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK.
  • Lei Zhang School of Mathematical Sciences, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, P.R. China.

DOI:

https://doi.org/10.4208/cicp.OA-2018-0169

Keywords:

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

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.

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Published

2020-03-06

Issue

Vol. 27 No. 1 (2020)

Section

Articles