Corpus ID: 18821705

Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice

@article{Ortner2011AnalysisOA,
  title={Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice},
  author={Christoph Ortner and Alexander V. Shapeev},
  journal={arXiv: Numerical Analysis},
  year={2011}
}
  • Christoph Ortner, Alexander V. Shapeev
  • Published 2011
  • Mathematics
  • arXiv: Numerical Analysis
  • We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy defects. The majority of the work is devoted to the analysis of consistency and stability of the method. These yield a priori error estimates in the H1-norm and the energy, which depend on the mesh size and the "smoothness" of the atomistic solution in the… CONTINUE READING

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