A posteriori error control for a quasi-continuum approximation of a periodic chain
C. Ortner and H. Wang
IMA Journal of Numerical Analysis, 34, 977–1001 (2014).


We consider a one-dimensional periodic atomistic model, for which we formulate and analyse an adaptive variant of a quasicontinuum method. We establish a posteriori error estimators 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.