IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2021y2021i1n8877012.html

A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid‐Poroelastic Structure Interaction Model

Author

Listed:
  • Houédanou Koffi Wilfrid

Abstract

In this work, we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in ℝd, d ∈ {2, 3}. The approach utilizes a Lagrange multiplier method to impose weakly the interface conditions [Ilona Ambartsumyan et al., Numerische Mathematik, 140 (2): 513‐553, 2018]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf‐sup conditions satisfied by the bilinear forms involved, Helmholtz decomposition, and local approximation properties of the Clément interpolant. On the other hand, inverse inequalities and the localization technique based on simplexe‐bubble and face‐bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

Suggested Citation

  • Houédanou Koffi Wilfrid, 2021. "A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid‐Poroelastic Structure Interaction Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:8877012
    DOI: 10.1155/2021/8877012
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2021/8877012
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2021/8877012?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
    ---><---

    References listed on IDEAS

    as
    1. Houédanou Koffi Wilfrid & Adetola Jamal & Allaoui Mohamed, 2020. "A Posteriori Error Analysis for a New Fully Mixed Isotropic Discretization of the Stationary Stokes‐Darcy Coupled Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    2. Houédanou Koffi Wilfrid & Adetola Jamal & Allaoui Mohamed, 2020. "A Posteriori Error Analysis for a New Fully Mixed Isotropic Discretization of the Stationary Stokes-Darcy Coupled Problem," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-12, October.
    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.

      More about this item

      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:wly:jnlaaa:v:2021:y:2021:i:1:n:8877012. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

      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.