High-order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo-Fabrizio fractional derivative

被引：19

作者：

Zhang, Min ^{[1
,2
]}

Liu, Yang ^{[2
]}

Li, Hong ^{[2
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen, Peoples R China

[2] Inner Mongolia Univ, Sch Math Sci, 235 West Daxue Rd, Hohhot 010021, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 35卷 / 04期

基金：

中国国家自然科学基金;

关键词：

a priori error analysis; Caputo-Fabrizio fractional derivative; fractal mobile; immobile transport equation; LDG method; stability; FINITE-ELEMENT-METHOD; SPECTRAL COLLOCATION METHOD; DIFFERENCE SCHEME; NUMERICAL-METHOD; DIFFUSION PROBLEM; VOLUME METHOD; APPROXIMATION; CONVERGENCE;

D O I：

10.1002/num.22366

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a local discontinuous Galerkin (LDG) method is studied for numerically solving the fractal mobile/immobile transport equation with a new time Caputo-Fabrizio fractional derivative. The stability of the LDG scheme is proven, and a priori error estimates with the second-order temporal convergence rate and the (k + 1)th order spatial convergence rate are derived in detail. Finally, numerical experiments based on P-k, k = 0, 1, 2, 3, elements are provided to verify our theoretical results.

引用

页码：1588 / 1612

页数：25

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