A priori and posteriori W-1, W-infinity error analysis of a QC method for complex lattices
A. Abdulle, P. Lin and A. V. Shapeev
SIAM Journal on Numerical Analysis, 51, 2357-2379 (2013).

ABSTRACT
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,W-infinity 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.