  We quantify the numerical error and modeling error associated with replacing
a nonlinear nonlocal bond-based peridynamic model with a local elasticity model
or a linearized peridynamics model away from the fracture set. The nonlocal
model treated here is characterized by a double well potential and is a smooth
version of the peridynamic model introduced in n Silling (J Mech Phys Solids
48(1), 2000). The solutions of nonlinear peridynamics are shown to converge to
the solution of linear elastodynamics at a rate linear with respect to the
length scale $\epsilon$ of non local interaction. This rate also holds for the
convergence of solutions of the linearized peridynamic model to the solution of
the local elastodynamic model. For local linear Lagrange interpolation the
consistency error for the numerical approximation is found to depend on the
ratio between mesh size $h$ and $\epsilon$. More generally for local Lagrange
interpolation of order $p\geq 1$ the consistency error is of order
$h^p/\epsilon$. A new stability theory for the time discretization is provided
and an explicit generalization of the CFL condition on the time step and its
relation to mesh size $h$ is given. Numerical simulations are provided
illustrating the consistency error associated with the convergence of nonlinear
and linearized peridynamics to linear elastodynamics.
