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

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. © 2010 American Mathematical Society.