Abstract
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 that our atomistic-continuum adaptivity algorithm computes the quantity of interest to within a given tolerance with a nearly minimal atomistic region.
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