A posteriori error control for a quasicontinuum approximation of a periodic chain
Provides rigorous error control for quasicontinuum methods, benefiting computational mechanics and materials science simulations.
The paper develops a posteriori error estimates for a quasicontinuum method applied to a 1D periodic atomistic chain, enabling adaptive mesh refinement. Numerical experiments demonstrate optimal convergence rates.
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.