IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v188y2021icp455-475.html
   My bibliography  Save this article

Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations

Author

Listed:
  • Wang, Yiran
  • Chung, Eric
  • Zhao, Lina

Abstract

In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the method is based on two multiscale spaces: pressure multiscale space and velocity multiscale space. The pressure space is constructed via a set of well-designed local spectral problems, which can be solved independently. Based on the computed pressure multiscale space, we will construct the velocity multiscale space by applying constrained energy minimization. The convergence of the proposed method is proved. In particular, we prove that the convergence of the method depends only on the coarse grid size, and is independent of the heterogeneities and contrast of the diffusion coefficient. Four typical types of permeability fields are exploited in the numerical simulations, and the results indicate that our proposed method works well and gives efficient and accurate numerical solutions.

Suggested Citation

  • Wang, Yiran & Chung, Eric & Zhao, Lina, 2021. "Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 455-475.
  • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:455-475
    DOI: 10.1016/j.matcom.2021.04.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421001348
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2021.04.016?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.

    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:188:y:2021:i:c:p:455-475. 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.