A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions
A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions
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DOI：
10.1016/j.amc.2019.124930
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
H. Tian;Jing Zhang;L. Ju
中科院分区：
文献类型：
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作者：
H. Tian;Jing Zhang;L. Ju
非局部扩散模型较好地描述了溶质在复杂介质中的扩散过程，而经典的偏微分方程理论却不能提供合适的描述。本文的目的是从理论和数值两个角度提供例证的计算非局部扩散模型的Legendre配置方法。与局部数值方法相比，Legendre配点法在计算区域规则且解足够光滑的情况下，能以较少的未知量达到固定的精度。本文是研究具有体积约束边界条件的非局部扩散方程的有效高阶方法，包括谱方法和谱元方法的基础。
The nonlocal diffusion model describes the diffusion process of solutes in complex media properly, while the classical theory of partial differential equations can not provide an appropriate description. The purpose of this paper is to provide illustrations from both theoretical and numerical perspectives of the computation of nonlocal diffusion models by Legendre collocation methods. Compared to local numerical methods, Legendre collocation methods can achieve a fixed accuracy with much fewer unknowns whenever the computational domain is regular and the solutions are sufficiently smooth. This paper is a groundwork towards efficient high order methods including spectral and spectral element methods for nonlocal diffusion equations with volume constrained boundary conditions.