Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: A two-dimensional model problem
C. Ortner and L. Zhang
SIAM Journal on Numerical Analysis, 50, 2940-2965 (2012).

ABSTRACT
We present a new variant of the geometry reconstruction approach for the
formulation of atomistic/continuum coupling methods (a/c methods). For many-body
nearest-neighbor interactions on the two-dimensional triangular lattice, we show
that patch test consistent a/c methods can be constructed for arbitrary
interface geometries. Moreover, we prove that all methods within this class are
first-order consistent at the atomistic/continuum interface and second-order
consistent in the interior of the continuum region.