ANALYSIS OF THE RESIDUAL-TYPE AND THE GRADIENT RECOVERY-TYPE A POSTERIORI ERROR ESTIMATORS FOR A CONSISTENT ATOMISTIC-TO-CONTINUUM COUPLING METHOD IN ONE-DIMENSION.

We consider the a posteriori error estimation for an atomistic-to-continuum coupling scheme for a generic one-dimensional many-body next-nearest-neighbor interaction model in one dimension. We derive and rigorously prove the efficiency of the residual type estimator. We prove the equivalence between the residual type and the gradient recovery-type estimator in the continuum region and propose a (novel) hybrid a posteriori error estimator by combining the two types of estimators. Our numerical experiments illustrate the optimal convergence rate of the adaptive algorithms using these estimators, whose effectivity indices are also presented. [ABSTRACT FROM AUTHOR]