IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v401y2021ics0096300321000692.html
   My bibliography  Save this article

The study of a continuous Galerkin method for Sobolev equation with space-time variable coefficients

Author

Listed:
  • Zhao, Zhihui
  • Li, Hong
  • Wang, Jing

Abstract

In this article, we will apply a space-time continuous Galerkin (CG) method to solve the numerical solution of Sobolev equation with space-time variable coefficients. Both the spatial and temporal variables of this method are discretized by finite element (FE) method, and hence it can easily attain the high order precision both in space and time directions as well as have the good stability. In addition, the variable spatial grid structures from one time span to the next and the time steps are permitted for this method, which are more suitable to design adaptive algorithm on unstructured mesh. We detailedly give the well-posed analysis of the numerical solution and the a priori error estimation in L∞(H1) norm without any restrictions on the space-time grid ratio. Finally, some numerical experiments are showed to conform the convergence orders and validate the high efficiency for the method investigated here.

Suggested Citation

  • Zhao, Zhihui & Li, Hong & Wang, Jing, 2021. "The study of a continuous Galerkin method for Sobolev equation with space-time variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321000692
    DOI: 10.1016/j.amc.2021.126021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321000692
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126021?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. Yimin Zhao, 2017. "Space as method," City, Taylor & Francis Journals, vol. 21(2), pages 190-206, March.
    2. Li, Xiaoli & Rui, Hongxing, 2019. "A block-centered finite difference method for the nonlinear Sobolev equation on nonuniform rectangular grids," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    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. Li, Meng & Wei, Yifan & Niu, Binqian & Zhao, Yong-Liang, 2022. "Fast L2-1σ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    2. Hao, Zhaopeng & Lin, Guang & Zhang, Zhongqiang, 2020. "Error estimates of a spectral Petrov–Galerkin method for two-sided fractional reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    3. Satti Wagistina & Dyah Rina Syafitri & Julaika Sri Lestari & Khoirunnisa Hafidha Amanatinismi & Dicky Setiawan & Santica Ramadhani, 2022. "Service Area Network Analysis for Location Planning of Microbusiness and Local Franchise in Urban Area: A Case Study in Malang City, East Java Provence, Indonesia," Economies, MDPI, vol. 10(5), pages 1-23, April.
    4. Yaxin Hou & Cao Wen & Hong Li & Yang Liu & Zhichao Fang & Yining Yang, 2020. "Some Second-Order σ Schemes Combined with an H 1 -Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    5. Kai Liu & Yu Liang & Hong S. He & Wen J. Wang & Chao Huang & Shengwei Zong & Lei Wang & Jiangtao Xiao & Haibo Du, 2018. "Long-Term Impacts of China’s New Commercial Harvest Exclusion Policy on Ecosystem Services and Biodiversity in the Temperate Forests of Northeast China," Sustainability, MDPI, vol. 10(4), pages 1-16, April.
    6. Seongwoo Jeon & Hyunjung Hong & Sungdae Kang, 2018. "Simulation of Urban Growth and Urban Living Environment with Release of the Green Belt," Sustainability, MDPI, vol. 10(9), pages 1-21, September.
    7. Marquart, Heike & Schlink, Uwe & Ueberham, Maximilian, 2020. "The planned and the perceived city: A comparison of cyclists' and decision-makers' views on cycling quality," Journal of Transport Geography, Elsevier, vol. 82(C).
    8. 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.

    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:401:y:2021:i:c:s0096300321000692. 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.