  We propose and analyze a goal-oriented a posteriori error estimator for the
atomistic-continuum modeling error in the quasicontinuum method. Based on this
error estimator, we develop an algorithm which adaptively determines the
atomistic and continuum regions to compute a quantity of interest to within a
given tolerance. We apply the algorithm to the computation of the structure of
a crystallographic defect described by a Frenkel-Kontorova model and present
the results of numerical experiments. The numerical results show that our
method gives an efficient estimate of the error and a nearly optimal
atomistic-continuum modeling strategy.
