# 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}
}
• Published 7 October 2012
• Mathematics
• SIAM J. Numer. Anal.
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…
4 Citations

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