In this paper, we propose nonlocal diffusion models with Dirichlet boundary. These nonlocal diffusion models preserve the maximum principle and also have corresponding variational form. With these good properties, we can prove the well-posedness and the vanishing nonlocality convergence. Furthermore, by specifically designed weight function, we can get a nonlocal diffusion model with second order convergence which is optimal for nonlocal diffusion models.

翻译：本文提出了具有狄利克雷边界的非局部扩散模型。这些非局部扩散模型保持了最大原理，同时具有相应的变分形式。基于这些良好特性，我们能够证明模型适定性及非局部性消失收敛。此外，通过特殊设计的权重函数，我们可以获得具有二阶收敛性的非局部扩散模型，这对于非局部扩散模型而言是最优收敛阶。