IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v182y2021icp838-857.html
   My bibliography  Save this article

Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution

Author

Listed:
  • Li, Changpin
  • Wang, Zhen

Abstract

In this paper, an efficient method seeking the numerical solution of a time-fractional convection equation whose solution is not smooth at the starting time is presented. The Caputo time-fractional derivative of order in (0,1) is discretized by the L1 finite difference method using non-uniform meshes; and, for the spatial derivative the discontinuous Galerkin (DG) finite element method is used. The stability and convergence of the method are analyzed for two-dimensional domains, using Cartesian and a particular class of unstructured grids. At last, several numerical examples are carried out which support the theoretical analysis.

Suggested Citation

  • Li, Changpin & Wang, Zhen, 2021. "Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 838-857.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:838-857
    DOI: 10.1016/j.matcom.2020.12.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420304626
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.12.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Changpin & Wang, Zhen, 2020. "The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 51-73.
    2. Shen, Jinye & Sun, Zhi-zhong & Cao, Wanrong, 2019. "A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 752-765.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Changpin & Li, Dongxia & Wang, Zhen, 2021. "L1/LDG method for the generalized time-fractional Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 357-378.
    2. Wei, Leilei & Li, Wenbo, 2021. "Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo–Fabrizio fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 280-290.
    3. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Changpin & Li, Dongxia & Wang, Zhen, 2021. "L1/LDG method for the generalized time-fractional Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 357-378.
    2. Wei, Leilei & Wang, Huanhuan, 2023. "Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 685-698.
    3. Yonggang Chen & Yu Qiao & Xiangtuan Xiong, 2022. "Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    4. Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.
    5. Gao, Xinghua & Yin, Baoli & Li, Hong & Liu, Yang, 2021. "TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 117-137.

    More about this item

    Keywords

    Time-fractional convection equation; L1 scheme; Discontinuous Galerkin method; Rectangular element; Triangular element;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:838-857. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.