A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
C. Ortner
Mathematics of Computation, 80, 1265-1285 (2011).

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.