  This paper studies numerical methods for accurate treatment of the interface
between the local and the nonlocal region in a QC approximation of atomistic
materials. Only the energy-based methods are considered. Particularly, a
quasicontinuum projection (QCP) method based on the idea of finite elements is
shown to be accurate and efficient for this problem. We analyse the QCP method
and study its relation to the existing methods, such as the quasinonlocal
quasicontinuum method and the geometrically consistent reconstruction-based
method. The analysis and the results of numerical tests confirm that the
projection-based QC method successfully removes the ghost force with the same
computational cost as the other methods. In all computed examples the error of
QCP is either the same or lower as the error of the other methods. The
performance of these methods in treating interfaces of elements in the local
region is also examined.
