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math.AP2024
A seamless local-nonlocal coupling diffusion model with vanishing nonlocality convergence
Yanzun Meng, Zuoqiang Shi
Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant…
math.NA2024
Asymptotically Compatible Error Bound of Finite Element Method for Nonlocal Diffusion Model with An Efficient Implementation
Yanzun Meng, Zuoqiang Shi
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes wi…
math.NA2024
A Second-Order Nonlocal Approximation to Manifold Poisson Models with Neumann Boundary
Yajie Zhang, Yanzun Meng, Zuoqiang Shi
In this paper, we propose a class of nonlocal models to approximate the Poisson model on manifolds with homogeneous Neumann boundary condition, where the manifolds are assumed to b…