IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v249y2026icp1022-1040.html

A class of oscillation-free discontinuous Galerkin methods for hyperbolic conservation laws

Author

Listed:
  • Kumar, Deepak
  • Rai, Pratima
  • Patel, Arvind

Abstract

In this paper, we introduce a class of oscillation-free discontinuous Galerkin schemes for solving hyperbolic conservation laws. The proposed schemes are based on hybridizing different spatial operators across different stages of the Runge–Kutta time integration. These schemes are built on oscillation-free discontinuous Galerkin method (Lu et al., 2021), which exhibits significant, provable properties such as L2-boundedness, superconvergence and conservation. The new class of schemes not only inherits the superconvergence, and conservation properties, but depending on the choice of hybridized operators, different variants possess other remarkable properties, such as a compact stencil, simplified boundary treatment, larger CFL numbers, and reduced floating-point operations as compared to the original method. Numerical experiments confirm that these schemes effectively suppress nonphysical oscillations when applied to nonlinear problems with discontinuous solutions. The accuracy and robustness of the proposed schemes are validated through standard benchmark problems.

Suggested Citation

  • Kumar, Deepak & Rai, Pratima & Patel, Arvind, 2026. "A class of oscillation-free discontinuous Galerkin methods for hyperbolic conservation laws," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 1022-1040.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:1022-1040
    DOI: 10.1016/j.matcom.2026.06.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426002648
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.06.020?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

    for a different version of it.

    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:eee:matcom:v:249:y:2026:i:c:p:1022-1040. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.