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arXiv · 1211.3346

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

Christoph Ortner·Hao Wang
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Abstract

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.

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Christoph Ortner, Hao Wang. 2012-11-14. A posteriori error control for a quasicontinuum approximation of a periodic chain. https://doi.org/10.1093/imanum%2Fdrt011

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