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, It is relatively easy to 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：本文提出了带Dirichlet边界的非局部扩散模型。这些非局部扩散模型既保持最大原理，又具有相应的变分形式。基于这些优良性质，可相对简单地证明模型的适定性和非局部性消失收敛性。此外，通过特别设计的权函数，我们获得了具有二阶收敛性的非局部扩散模型，该收敛阶对非局部扩散模型而言是最优的。