  This work considers the nodal finite element approximation of peridynamics,
in which the nodal displacements satisfy the peridynamics equation at each mesh
node. For the nonlinear bond-based peridynamics model, it is shown that, under
the suitable assumptions on an exact solution, the discretized solution
associated with the central-in-time and nodal finite element discretization
converges to the exact solution in $L^2$ norm at the rate $C_1 \Delta t + C_2
h^2/\epsilon^2$. Here, $\Delta t$, $h$, and $\epsilon$ are time step size, mesh
size, and the size of the horizon or nonlocal length scale, respectively.
Constants $C_1$ and $C_2$ are independent of $h$ and $\Delta t$ and depend on
the norms of the exact solution. Several numerical examples involving
pre-crack, void, and notch are considered, and the efficacy of the proposed
nodal finite element discretization is analyzed.
