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For a next-nearest neighbour pair interaction model in a periodic domain, apriori and a posteriori analyses of the quasinonlocal quasicontinuum method(QNL-QC) are presented. The results are valid for large deformations andessentially guarantee a one-to-one correspondence between atomistic solutionsand QNL-QC solutions. The analysis is based on truncation error and residualestimates in negative norms and novel a priori and a posteriori stabilityestimates.

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