  In this paper we construct energy based numerical methods free of ghost
forces in three dimensional lattices arising in crystalline materials. The
analysis hinges on establishing a connection of the coupled system to
conforming finite elements. Key ingredients are: (i) a new representation of
discrete derivatives related to long range interactions of atoms as volume
integrals of gradients of piecewise linear functions over bond volumes, and
(ii) the construction of an underlying globally continuous function
representing the coupled modeling method.
