  We analyze a force-based quasicontinuum approximation to a one-dimensional
system of atoms that interact by a classical atomistic potential. This
force-based quasicontinuum approximation is derived as the modification of an
energy-based quasicontinuum approximation by the addition of nonconservative
forces to correct nonphysical ``ghost'' forces that occur in the atomistic to
continuum interface.
  We prove that the force-based quasicontinuum equations have a unique solution
under suitable restrictions on the loads. For Lennard-Jones
next-nearest-neighbor interactions, we show that unique solutions exist for
loads in a symmetric region extending nearly to the tensile limit.
  We give an analysis of the convergence of the ghost force iteration method to
solve the equilibrium equations for the force-based quasicontinuum
approximation. We show that the ghost force iteration is a contraction and give
an analysis for its convergence rate.
