IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v262y2015icp56-78.html
   My bibliography  Save this article

Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method

Author

Listed:
  • Li, Xiaolin
  • Chen, Hao
  • Wang, Yan

Abstract

The improved moving least-square (IMLS) approximation is a method to form shape functions in meshless methods. For the application of IMLS-based meshless methods to the numerical solution of boundary value problems, it is fundamental to analyze error of the IMLS approximation in Sobolev spaces. This paper begins by discussing properties of the IMLS shape function. Under appropriate assumption on weight functions, error estimates for the IMLS approximation are then established in Sobolev spaces in multiple dimensions. The improved element-free Galerkin (IEFG) method is a typical meshless Galerkin method based on coupling the IMLS approximation and Galerkin weak form. Error analysis of the IEFG method is also provided. Numerical examples are finally presented to prove the theoretical error results.

Suggested Citation

  • Li, Xiaolin & Chen, Hao & Wang, Yan, 2015. "Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 56-78.
  • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:56-78
    DOI: 10.1016/j.amc.2015.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315004282
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2015.04.002?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, Xiaolin, 2011. "Development of a meshless Galerkin boundary node method for viscous fluid flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 258-280.
    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. Qu, Wenzhen & Sun, Linlin & Li, Po-Wei, 2021. "Bending analysis of simply supported and clamped thin elastic plates by using a modified version of the LMFS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 347-357.
    2. Zhang, Tao & Li, Xiaolin, 2020. "Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    3. Sun, FengXin & Wang, JuFeng, 2017. "Interpolating element-free Galerkin method for the regularized long wave equation and its error analysis," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 54-69.
    4. Shirzadi, Mohammad & Rostami, Mohammadreza & Dehghan, Mehdi & Li, Xiaolin, 2023. "American options pricing under regime-switching jump-diffusion models with meshfree finite point method," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Zhijuan Meng & Xiaofei Chi & Lidong Ma, 2022. "A Hybrid Interpolating Meshless Method for 3D Advection–Diffusion Problems," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    6. Wang, Qiao & Zhou, Wei & Feng, Y.T. & Ma, Gang & Cheng, Yonggang & Chang, Xiaolin, 2019. "An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 347-370.

    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. Qu, Wenzhen & Chen, Wen & Fu, Zhuojia & Gu, Yan, 2018. "Fast multipole singular boundary method for Stokes flow problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 57-69.

    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:262:y:2015:i:c:p:56-78. 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: 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.