Goal-oriented atomistic-continuum adaptivity for the quasicontinuum approximation

Marcel Arndt, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova-type model.

Original languageEnglish (US)
Pages (from-to)407-415
Number of pages9
JournalInternational Journal for Multiscale Computational Engineering
Issue number5
StatePublished - Dec 1 2007


  • A posteriori
  • Atomistic-continuum
  • Defect
  • Dislocation
  • Error estimation
  • Frenkel-Kontorova
  • Goal-oriented
  • Quasicontinuum


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