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
收藏
页码：1588 / 1612
页数：25
相关论文
共 50 条
  • [21] A NEW NUMERICAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS IN THE SENSE OF CAPUTO-FABRIZIO DERIVATIVE
    Herik, Leila Moghadam Dizaj
    Javidi, Mohammad
    Shafiee, Mahmoud
    FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2022, 37 (01): : 51 - 66
  • [22] Well-posedness of an initial value problem for fractional diffusion equation with Caputo-Fabrizio derivative
    Nguyen Huy Tuan
    Zhou, Yong
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 375
  • [23] A high-order nodal discontinuous Galerkin method for a linearized fractional Cahn-Hilliard equation
    Aboelenen, Tarek
    El-Hawary, H. M.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) : 1197 - 1217
  • [24] Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo-Fabrizio fractional derivative
    Qiao, Haili
    Liu, Zhengguang
    Cheng, Aijie
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [25] Numerical approach of Fokker-Planck equation with Caputo-Fabrizio fractional derivative using Ritz approximation
    Firoozjaee, M. A.
    Jafari, H.
    Lia, A.
    Baleanu, D.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 339 : 367 - 373
  • [26] Stability analysis of fractional-order linear system with time delay described by the Caputo-Fabrizio derivative
    Li, Hong
    Zhong, Shou-ming
    Cheng, Jun
    Li, Hou-biao
    ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
  • [27] High-order local discontinuous Galerkin method for simulating wormhole propagation
    Guo, Hui
    Tian, Lulu
    Xu, Ziyao
    Yang, Yang
    Qi, Ning
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 350 : 247 - 261
  • [28] Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation
    Du, Yanwei
    Liu, Yang
    Li, Hong
    Fang, Zhichao
    He, Siriguleng
    JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 344 : 108 - 126
  • [29] Local discontinuous Galerkin method based on a family of second-order time approximation schemes for fractional mobile/immobile convection-diffusion equations
    Niu, Yuxuan
    Wang, Jinfeng
    Liu, Yang
    Li, Hong
    Fang, Zhichao
    APPLIED NUMERICAL MATHEMATICS, 2022, 179 : 149 - 169
  • [30] Dynamical analysis and chaos synchronization of a fractional-order novel financial model based on Caputo-Fabrizio derivative
    Al-khedhairi, A.
    EUROPEAN PHYSICAL JOURNAL PLUS, 2019, 134 (10)
12345