In this paper we prove a priori and a posteriori error estimates for a multiscale numerical method for computing equilibria of multilattices under an external force. The error estimates are derived in a W1,∞ 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). We illustrate our error estimates with numerical experiments.
@article{arxiv.1210.2076,
title = {A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices},
author = {Assyr Abdulle and Ping Lin and Alexander V. Shapeev},
journal= {arXiv preprint arXiv:1210.2076},
year = {2012}
}