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：在本文中，我们提出了带有Dirichlet边界的非局域扩散模型。这些非局域扩散模型保留了最大值原理，并具有相应的变分形式。凭借这些优良性质，可以较为容易地证明其适定性与非局域性消失收敛性。此外，通过专门设计的权函数，我们能够获得具有二阶收敛精度的非局域扩散模型——这对于非局域扩散模型而言是最优的。