  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 $W^{1,\infty}$ 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). We
illustrate our error estimates with numerical experiments.
