A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method   for complex lattices
  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. 
Assyr Abdulle, Ping Lin, Alexander V. Shapeev
math.NA