On the extension of goal-oriented error estimation and hierarchical modeling to discrete lattice models

The Goals algorithm for adaptive modeling is extended to the case of discrete models such as those characterized by lattice structures (or the static behavior molecular systems) by using surrogate models obtained from continuum approximations of the lattice. The result is a technique that could provide for scale-bridging between continuum models and atomistic models, although the present development concerns only simple algebraic systems. An example is provided in which quantities of interest in system with a large number of degrees of freedom are computed to a preset tolerance in relatively few low-order approximations.