A priori error estimates for energy-based quasicontinuum approximations of a periodic chain
C. Ortner and H. Wang
Mathematica Models & Methods in Applied Sciences, 21, 2491–2521 (2011).


We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasinonlocal QC method. Our analysis decomposes the consistency error into modeling and coarsening errors. While previous results on estimating the modeling error exist, we present a new and simpler proof based on negative-norm estimates. Our stability analysis extends previous results on sharp stability estimates under homogeneous strain to the nonlinear setting. Finally, we present numerical experiments to illustrate the results of our analysis.