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.

翻译：本文研究了近场动力学的节点有限元逼近方法，其中节点位移在每个网格节点处满足近场动力学方程。针对基于非线性键的近场动力学模型，在精确解满足适当假设的条件下，证明与时间中心差分和节点有限元离散相关的离散化解在$L^2$范数下以速率$C_1 \Delta t + C_2 h^2/\epsilon^2$收敛于精确解。此处，$\Delta t$、$h$和$\epsilon$分别表示时间步长、网格尺寸和近场范围（即非局部长度尺度）。常数$C_1$和$C_2$独立于$h$和$\Delta t$，且依赖于精确解的范数。论文考虑了含初始裂纹、空洞和切口的多个数值算例，并分析了所提出节点有限元离散方法的有效性。