Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations

Yunzhe Tao, Xiaochuan Tian and Qiang Du

Applied Mathematics and Computation, 2017, vol. 305, issue C, 282-298

Abstract: This paper studies nonlocal diffusion models associated with a finite nonlocal horizon parameter δ that characterizes the range of nonlocal interactions. The focus is on the variational formulation associated with Neumann type constraints and its numerical approximations. We establish the well-posedness for some variational problems associated and study their local limit as δ → 0. A main contribution is to derive a second order convergence to the local limit. We then discuss the numerical approximations including standard finite element methods and quadrature based finite difference methods. We study their convergence in the nonlocal setting and in the local limit.

Keywords: Nonlocal diffusion; Peridynamic model; Nonlocal operator; Neumann problems; Finite element; Finite difference (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:305:y:2017:i:c:p:282-298

DOI: 10.1016/j.amc.2017.01.061

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