IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v389y2021ics0096300320305282.html
   My bibliography  Save this article

Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping

Author

Listed:
  • Li, Zhenzhen
  • Li, Minghao
  • Shi, Dongyang

Abstract

In this paper, the linearized backward Euler scheme for the transient Stokes equations with damping is presented, in which the velocity and pressure are approximated by the lowest-order Bernadi-Raugel rectangular element pair. Unconditional optimal error estimates of the velocity in the norms L∞(L2) and L∞(H1), and the pressure in the norm L∞(L2) are derived through the Stokes operator and the H−1-norm estimate. Moreover, the superclose properties and global superconvergent results are obtained by the interpolation post-processing technique. Finally, some numerical results are provided to confirm the theoretical analysis.

Suggested Citation

  • Li, Zhenzhen & Li, Minghao & Shi, Dongyang, 2021. "Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    • Handle: RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305282
    DOI: 10.1016/j.amc.2020.125572
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320305282
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125572?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. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 216-226.
    2. Shi, Dongyang & Yang, Huaijun, 2017. "Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 40-47.
    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. Wu, Yanmi & Shi, Dongyang, 2021. "Quasi-uniform and unconditional superconvergence analysis of Ciarlet–Raviart scheme for the fourth order singularly perturbed Bi-wave problem modeling d-wave superconductors," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    2. Xu, Chao & Shi, Dongyang, 2019. "Superconvergence analysis of low order nonconforming finite element methods for variational inequality problem with displacement obstacle," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 1-11.
    3. Pei, Lifang & Zhang, Chaofeng & Shi, Dongyang, 2024. "Unconditional superconvergence analysis of two-grid nonconforming FEMs for the fourth order nonlinear extend Fisher-Kolmogorov equation," Applied Mathematics and Computation, Elsevier, vol. 471(C).
    4. 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).
    5. Gong, Yujie & Yuan, Guangwei & Cui, Xia, 2024. "Analysis on a high accuracy fully implicit solution for strong nonlinear diffusion problem - convergence, stability, and uniqueness," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    6. Shi, Dongyang & Yang, Huaijun, 2019. "Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 210-224.
    7. Zhang, Houchao & Shi, Dongyang & Li, Qingfu, 2020. "Nonconforming finite element method for a generalized nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    8. Shi, Dongyang & Wu, Yanmi, 2020. "Uniformly superconvergent analysis of an efficient two-grid method for nonlinear Bi-wave singular perturbation problem," Applied Mathematics and Computation, Elsevier, vol. 367(C).

    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:389:y:2021:i:c:s0096300320305282. 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.