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 (Lead / Corresponding author)

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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.

Original languageEnglish
Pages (from-to)198-226
Number of pages29
JournalCommunications in Computational Physics
Issue number1
Early online date31 Oct 2019
Publication statusPublished - 2020



  • A posteriori error estimate
  • Atomistic models
  • Atomistic-to-continuum coupling
  • Coarse graining
  • Quasicontinuum method

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