A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D
This work offers rigorous error bounds for a specific multiscale method, but its 1D setting and next-nearest neighbor model limit its immediate impact.
The paper provides a priori and a posteriori error analyses for the quasinonlocal quasicontinuum method (QNL-QC) in 1D, proving a one-to-one correspondence between atomistic and QNL-QC solutions under large deformations.
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.