TY - JOUR
T1 - A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization
AU - Bi , Mingchao
AU - Ju , Lili
AU - Tian , Hao
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 990
EP - 1008
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2022-0004s 
UR - https://global-sci.org/intro/article_detail/nmtma/21087.html
KW - Nonlocal diffusion, dual-horizon, maximum principle, finite element discretization, asymptotically compatible.
AB - <p style="text-align: justify;">In this paper, we present a dual-horizon nonlocal diffusion model, in
which the influence area at each point consists of a standard sphere horizon and
an irregular dual horizon and its geometry is determined by the distribution of the
varying horizon parameter. We prove the mass conservation and maximum principle
of the proposed nonlocal model, and establish its well-posedness and convergence
to the classical diffusion model. Noticing that the dual horizon-related term in fact
vanishes in the corresponding variational form of the model, we then propose a finite
element discretization for its numerical solution, which avoids the difficulty of accurate calculations of integrals on irregular intersection regions between the mesh
elements and the dual horizons. Various numerical experiments in two and three
dimensions are also performed to illustrate the usage of the variable horizon and
demonstrate the effectiveness of the numerical scheme.</p>