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.