Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

Details Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

2007-07-31

arxiv.org/abs/0708.0025v1

Mathematics

Numerical Analysis

9 pages, 2 figures

Scientific paper

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.

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