  We investigate two examples of node-based cluster summation rules that have
been proposed for the quasicontinuum method: a force-based approach (Knap &
Ortiz, J. Mech. Phys. Solids 49, 2001), and an energy-based approach which is a
generalization of the non-local quasicontinuum method (Eidel & Stukowski, J.
Mech. Phys. Solids, to appear). We show that, even for the case of nearest
neighbour interaction in a one-dimensional periodic chain, both of these
approaches create large errors when used with graded and, more generally,
non-smooth meshes. These errors cannot be removed by increasing the cluster
size. We offer some suggestions how the accuracy of (cluster) summation rules
may be improved.
