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


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.