IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v10y2018i4p136.html
   My bibliography  Save this article

A Petrov-Galerkin Finite Element Method for Solving the Time-fractional Diffusion Equation with Interface

Author

Listed:
  • Liwei Shi

Abstract

Time-fractional partial differential equation is widely applied in a variety of disciplines, its numerical solution has attracted much attention from researchers in recent years. Time-fractional differential equations with interfaces is a more challenging problem because the governing equation has discontinuous coefficients at interfaces and sometimes singular source term exists. In this paper, we propose a Petrov-Galerkin finite element method for solving the two-dimensional time-fractional diffusion equation with interfaces. In this method, a finite difference scheme is employed in time and a Petrov-Galerkin finite element method is employed in space. Extensive numerical experiments show that for a fractional diffusion equation of order $\alpha$ with interfaces, our method gets to $(2-\alpha)$-order accurate in the $L^2$ and $L^{\infty}$ norm.

Suggested Citation

  • Liwei Shi, 2018. "A Petrov-Galerkin Finite Element Method for Solving the Time-fractional Diffusion Equation with Interface," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(4), pages 136-150, August.
  • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:4:p:136
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/download/76665/42425
    Download Restriction: no

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/76665
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Baeumer, B. & Benson, D.A. & Meerschaert, M.M., 2005. "Advection and dispersion in time and space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 245-262.
    Full references (including those not matched with items on IDEAS)

    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. Fernandez-Anaya, G. & Valdes-Parada, F.J. & Alvarez-Ramirez, J., 2011. "On generalized fractional Cattaneo’s equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4198-4202.
    2. Baeumer, B. & Meerschaert, M.M., 2007. "Fractional diffusion with two time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 237-251.
    3. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
    4. Wei, Song & Chen, Wen & Hon, Y.C., 2016. "Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1244-1251.
    5. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.

    More about this item

    Keywords

    time-fractional partial differential equation; sharp-edged interface; Petrov-Galerkin finite element method; finite difference method;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    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:ibn:jmrjnl:v:10:y:2018:i:4:p:136. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    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.