IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v257y2015icp553-565.html
   My bibliography  Save this article

Finite element method for two-dimensional space-fractional advection–dispersion equations

Author

Listed:
  • Zhao, Yanmin
  • Bu, Weiping
  • Huang, Jianfei
  • Liu, Da-Yan
  • Tang, Yifa

Abstract

The backward Euler and Crank–Nicolson–Galerkin fully-discrete approximate schemes for two-dimensional space-fractional advection–dispersion equations are established. Firstly, we prove that the corresponding variational problem has a unique solution, and the proposed fully-discrete schemes are unconditionally stable, whose solutions are all unique. Secondly, the optimal error estimates are derived by use of properties of projection operator and fractional derivatives. Finally, numerical examples demonstrate effectiveness of numerical schemes and confirm the theoretical analysis.

Suggested Citation

  • Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:553-565
    DOI: 10.1016/j.amc.2015.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315000302
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.01.016?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.

    Citations

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


    Cited by:

    1. She, Zi-Hang & Qiu, Li-Min & Qu, Wei, 2023. "An unconditionally convergent RSCSCS iteration method for Riesz space fractional diffusion equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 633-646.
    2. Yang, Hong & Lao, Cheng-Xue & She, Zi-Hang, 2023. "Fast solution methods for Riesz space fractional diffusion equations with non-separable coefficients," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    3. Zhao, Jingjun & Zhao, Wenjiao & Xu, Yang, 2021. "Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    4. Eyaya Fekadie Anley & Zhoushun Zheng, 2020. "Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term," Mathematics, MDPI, vol. 8(11), pages 1-27, October.
    5. Zhao, Jingjun & Zhao, Wenjiao & Xu, Yang, 2023. "Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    6. Shi, Z.G. & Zhao, Y.M. & Liu, F. & Wang, F.L. & Tang, Y.F., 2018. "Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 290-304.
    7. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    8. Zieniuk, Eugeniusz, 2017. "Approximation of the derivatives of solutions in a normalized domain for 2D solids using the PIES methodAuthor-Name: Bołtuć, Agnieszka," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 138-155.
    9. Mohammed M. Al-Shomrani & Mohamed A. Abdelkawy & António M. Lopes, 2023. "Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    10. Saffarian, Marziyeh & Mohebbi, Akbar, 2022. "Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 348-370.
    11. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    12. Qu, Wei & Li, Zhi, 2021. "Fast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    13. Jie Zhao & Hong Li & Zhichao Fang & Yang Liu, 2019. "A Mixed Finite Volume Element Method for Time-Fractional Reaction-Diffusion Equations on Triangular Grids," Mathematics, MDPI, vol. 7(7), pages 1-18, July.

    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:apmaco:v:257:y:2015:i:c:p:553-565. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.