A Priori and A Posteriori W1, INFINITY Error Analysis of a QC Method for Complex Lattices

@article{Abdulle2013APA,
  title={A Priori and A Posteriori W1, INFINITY Error Analysis of a QC Method for Complex Lattices},
  author={Assyr Abdulle and Ping Lin and Alexander V. Shapeev},
  journal={SIAM J. Numer. Anal.},
  year={2013},
  volume={51},
  pages={2357-2379}
}
In this paper we derive regularity results for equilibria of multilattices under an external force and prove a priori and a posteriori error estimates for a multiscale numerical method for computing such equilibria. The estimates are derived in a $W^{1,\infty}$ norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori… 

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