We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual and stability estimates. We formulate adaptive mesh refinement algorithms based on these error estimators. Our numerical experiments indicate optimal convergence rates of these algorithms.
@article{arxiv.1211.3346,
title = {A posteriori error control for a quasicontinuum approximation of a periodic chain},
author = {Christoph Ortner and Hao Wang},
journal= {arXiv preprint arXiv:1211.3346},
year = {2017}
}