IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4614-7828-7_15.html
   My bibliography  Save this book chapter

Numerical Solutions of the 1D Convection–Diffusion–Reaction and the Burgers Equation Using Implicit Multi-stage and Finite Element Methods

In: Integral Methods in Science and Engineering

Author

Listed:
  • C. A. Ladeia

    (State University of Londrina)

  • N. M. L. Romeiro

    (State University of Londrina)

Abstract

In this work we apply the semi-discrete formulation, where the time variable is discretized using an implicit multi-stage method and the space variable is discretized using the finite element method, to obtain numerical solutions for the 1D convection–diffusion–reaction and the Burgers equation, whose analytical solutions are known. More specifically, we use the implicit multi-stage method of second and fourth-order for time discretization. For space discretization, we use three finite elements methods, least square (LSFEM), Galerkin (GFEM) and streamline-upwind Petrov-Galerkin (SUPG). We present an error analysis, comparing the numerical with analytical solutions. We verify that the implicit multi-stage second-order method when combined with the LSFEM, GFEM and SUPG, increased the region of convergence of the numerical solutions. LSFEM presented the better performance when compared to GFEM and SUPG.

Suggested Citation

  • C. A. Ladeia & N. M. L. Romeiro, 2013. "Numerical Solutions of the 1D Convection–Diffusion–Reaction and the Burgers Equation Using Implicit Multi-stage and Finite Element Methods," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Haroldo F. de Campos Velho (ed.), Integral Methods in Science and Engineering, edition 127, chapter 0, pages 205-216, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7828-7_15
    DOI: 10.1007/978-1-4614-7828-7_15
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:spr:sprchp:978-1-4614-7828-7_15. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.