  The quasicontinuum approximation is a method to reduce the atomistic degrees
of freedom of a crystalline solid by piecewise linear interpolation from
representative atoms that are nodes for a finite element triangulation. In
regions of the crystal with a highly nonuniform deformation such as around
defects, every atom must be a representative atom to obtain sufficient
accuracy, but the mesh can be coarsened away from such regions to remove
atomistic degrees of freedom while retaining sufficient accuracy. We present an
error estimator and a related adaptive mesh refinement algorithm for the
quasicontinuum approximation of a generalized Frenkel-Kontorova model that
enables a quantity of interest to be efficiently computed to a predetermined
accuracy.
