A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions

Haochen Wang, Mingjie Liao, Ping Lin, Lei Zhang (Lead / Corresponding author)

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
125 Downloads (Pure)

Abstract

Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the residual, the stability constant, and the error bound, for a consistent atomistic/continuum coupling method in 2D. We design and implement the corresponding adaptive mesh refinement algorithm, and the convergence rate with respect to degrees of freedom is optimal compare with a priori error estimates.
Original languageEnglish
Pages (from-to)A2087-A2119
Number of pages33
JournalSIAM Journal on Scientific Computing
Volume40
Issue number4
Early online date5 Jul 2018
DOIs
Publication statusPublished - 2018

Keywords

  • atomistic models
  • coarse graining
  • atomistic-to-continuum coupling
  • adaptive algorithm
  • a posteriori error estimate

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