A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D

Details A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D

2009-11-03

arxiv.org/abs/0911.0671v2

Mathematics

Numerical Analysis

Scientific paper

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 truncation error and residual estimates in negative norms and novel a priori and a posteriori stability estimates.

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