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Adaptive atomistic/continuum (a/c) coupling method is an important method forthe simulation of material and atomistic systems with defects to achieve thebalance of accuracy and efficiency. Residual based a posteriori error estimatoris often employed in the adaptive algorithm to provide an estimate of the errorof the strain committed by applying the continuum approximation for theatomistic system and the finite element discretization in the continuum region.In this work, we propose a theory based approximation for the residual based aposteriori error estimator which greatly improves the efficiency of theadaptivity. In particular, the numerically expensive modeling residual is onlycomputed exactly in a small region around the coupling interface but replacedby a theoretically justified approximation by the coarsening residual outsidethat region. We present a range of adaptive computations based on our modifieda posteriori error estimator and its variants for different types ofcrystalline defects some of which are not considered in previous relatedliterature of the adaptive a/c methods. The numerical results show that,compared with the original residual based error estimator, the adaptivealgorithm using the modified error estimator with properly chosen parametersleads to the same optimal convergence rate of the error but reduces thecomputational cost by one order with respect to the number of degrees offreedom.

Efficient a Posteriori Error Control of a Consistent Atomistic/Continuum Coupling Method for Two Dimensional Crystalline Defects