A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D

Ortner, Christoph

doi:10.1090/S0025-5718-2010-02453-6

A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
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by Christoph Ortner;

Math. Comp. 80 (2011), 1265-1285

DOI: https://doi.org/10.1090/S0025-5718-2010-02453-6

Published electronically: December 31, 2010

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Abstract:

For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially guarantee a one-to-one correspondence between atomistic solutions and QNL-QC solutions. The analysis is based on consistency error estimates in negative norms, novel a priori and a posteriori stability estimates, and a quantitative inverse function theorem.

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