Numerische Mathematik

, Volume 140, Issue 3, pp 703–754 | Cite as

Force-based atomistic/continuum blending for multilattices

  • Derek OlsonEmail author
  • Xingjie Li
  • Christoph Ortner
  • Brian Van Koten


We formulate the blended force-based quasicontinuum method for multilattices and develop rigorous error estimates in terms of the approximation parameters: choice of atomistic region, blending region, and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone–Wales defect in graphene.

Mathematics Subject Classification

65N12 74S30 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Derek Olson
    • 1
    Email author
  • Xingjie Li
    • 2
  • Christoph Ortner
    • 3
  • Brian Van Koten
    • 4
  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Mathematics and StatisticsUniversity of North Carolina-CharlotteCharlotteUSA
  3. 3.Mathematics InstituteUniversity of WarwickCoventryUK
  4. 4.Department of StatisticsUniversity of ChicagoChicagoUSA

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