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We consider a 1D periodic atomistic model, for which we formulate and analyzean adaptive variant of a quasicontinuum method. We establish a posteriori errorestimates for the energy norm and for the energy, based on a posterioriresidual and stability estimates. We formulate adaptive mesh refinementalgorithms based on these error estimators. Our numerical experiments indicateoptimal convergence rates of these algorithms.

A posteriori error control for a quasicontinuum approximation of a periodic chain