Error control for molecular statics problems
S. Prudhomme, P. T. Bauman and J. T. Oden
International Journal for Multiscale Computational Engineering, 4, 647-662 (2006).

ABSTRACT
In this paper, we present an extension of goal-oriented error estimation and
adaptation to the simulation of multiscale problems of molecular statics.
Computable error estimates for the quasicontinuum method arc developed with
respect to specific quantities of interest, and an adaptive strategy based on
these estimates is proposed for error control. The theoretical results are
illustrated on a nanoindentation problem in which the quantity of interest is
the force acting on the indenter. The promising capability of such error
estimates and adaptive procedure for the solution of multiscale problems is
demonstrated on numerical examples.