Goal-oriented atomistic-continuum adaptivity for the quasicontinuum approximation
M. Arndt and M. Luskin
International Journal for Multiscale Computational Engineering, 5, 407-415 (2007).

ABSTRACT
We give a goal-oriented a posteriori error estimator for the atomistic-continuum
modeling error in the quasicontinuum method, and we use this estimator to design
an adaptive algorithm to compute a quantity of interest to a given tolerance by
using a nearly minimal number of atomistic degrees of freedom. We present
computational results that demonstrate the effectiveness of our algorithm for a
periodic array of dislocations described by a Frenkel-Kontorova-type model.