A posteriori error control for a quasicontinuum approximation of a periodic chain

TL;DR

This paper develops an adaptive quasicontinuum method for a 1D periodic atomistic model, providing a posteriori error estimates and demonstrating optimal convergence through numerical experiments.

Contribution

It introduces an adaptive variant of the quasicontinuum method with proven a posteriori error estimates for energy and energy norm in a 1D periodic setting.

Findings

Optimal convergence rates achieved in numerical experiments

Effective a posteriori residual and stability-based error estimators

Adaptive mesh refinement improves accuracy efficiently

Abstract

We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual and stability estimates. We formulate adaptive mesh refinement algorithms based on these error estimators. Our numerical experiments indicate optimal convergence rates of these algorithms.