Maximum principle preserving nonlocal diffusion model with Dirichlet boundary condition

TL;DR

This paper introduces a nonlocal diffusion model with Dirichlet boundary conditions that preserves the maximum principle, ensures well-posedness, and achieves optimal second-order convergence through a specially designed weight function.

Contribution

It presents a novel nonlocal diffusion model with maximum principle preservation, variational form, and optimal convergence properties, advancing the theoretical understanding and numerical accuracy of nonlocal models.

Findings

Model preserves maximum principle

Proves well-posedness and convergence

Achieves second-order convergence with specific weights

Abstract

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.