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We consider the problem of a posteriori error estimates and adaptivity for three typical force-based atomistic-to-continuum coupling methods. Combining the residual and the stability estimates, we derive computable a posteriori error estimators for the three methods in the energy norm and formulate adaptive algorithms using these estimators. Our numerical experiments show optimal convergence rates of these algorithms. The efficiency of the estimators are also demonstrated numerically. AMS subject classifications: 65N12, 65N15, 70C20, 82D25

A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain