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).


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.