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In this paper, we develop the residual based a posteriori error estimates andthe corresponding adaptive mesh refinement algorithm for atomistic/continuum(a/c) coupling with finite range interactions in two dimensions. We havesystematically derived a new explicitly computable stress tensor formula forfinite range interactions. In particular, we use the geometric reconstructionbased consistent atomistic/continuum (GRAC) coupling scheme, which is optimalif the continuum model is discretized by $P^1$ finite elements. The numericalresults of the adaptive mesh refinement algorithm is consistent with theoptimal a priori error estimates.

A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions