  Atomistic/continuum coupling methods aim to achieve optimal balance between
accuracy and efficiency. Adaptivity is the key for the efficient implementation
of such methods. In this paper, we carry out a rigorous a posteriori analysis
of the residual, the stability constant, and the error bound, for a consistent
atomistic/continuum coupling method in 2D. We design and implement the
corresponding adaptive mesh refinement algorithm, and the convergence rate with
respect to degrees of freedom is optimal compare with a priori error estimates.
