  We study a force-based hybrid method that couples atomistic models with
nonlinear Cauchy-Born elasticity models. We show that the proposed scheme
converges quadratically to the solution of the atomistic model, as the ratio
between lattice parameter and the characteristic length scale of the
deformation tends to zero. Convergence is established for general short-ranged
atomistic potential and for simple lattices in three dimension. The convergence
is based on consistency and stability analysis. General tools are developed in
the framework of pseudo-difference operators for stability analysis in
arbitrary dimension of the multiscale atomistic and continuum coupling methods.
