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Christoph Ortner, Endre Süli:A-priori analysis of the quasicontinuum method in one dimensionThe quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we give an a-priori error analysis for the quasicontinuum method in one dimension. We consider atomistic models with Lennard-Jones type long range interactions and a practical QC formulation. First, we prove the existence, the local uniqueness and the stability with respect to discrete $W^{1,\infty}$-norm of elastic and fractured atomistic solutions. We then used a fixed point technique to prove the existence of quasicontinuum approximation which satisfies an optimal a-priori error bound.Bibliographical note: submitted to ESAIM:M2AN. |