Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model

Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model

Year:    2016

East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 1 : pp. 60–79

Abstract

Two-grid finite element methods for the steady Navier-Stokes/Darcy model are considered. Stability and optimal error estimates in the $H^1$-norm for velocity and piezometric approximations and the $L^2$-norm for pressure are established under mesh sizes satisfying $h=H^2$. A modified decoupled and linearised two-grid algorithm is developed, together with some associated optimal error estimates. Our method and results extend and improve an earlier investigation, and some numerical computations illustrate the efficiency and effectiveness of the new algorithm.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.080215.111215a

East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 1 : pp. 60–79

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Navier-Stokes equations Darcy’s law multimodeling problems two-grid method.

  1. Two-Grid Stabilized Lowest Equal-Order Finite Element Method for the Dual-Permeability-Stokes Fluid Flow Model

    Haque, Md Nazmul | Nasu, Nasrin Jahan | Al Mahbub, Md. Abdullah | Mohebujjaman, Muhammad

    Journal of Scientific Computing, Vol. 102 (2025), Iss. 1

    https://doi.org/10.1007/s10915-024-02723-x [Citations: 0]
  2. An Adaptive Time Filter Algorithm with Different Subdomain Time Steps for Super-Hydrophobic Proppants Based on the 3D Unsteady-State Triple-Porosity Stokes Model

    Li, Jian | Song, Wenyan | Qin, Yi | Chen, Zhangxing

    Journal of Scientific Computing, Vol. 101 (2024), Iss. 3

    https://doi.org/10.1007/s10915-024-02716-w [Citations: 0]
  3. Decoupled characteristic stabilized finite element method for time‐dependent Navier–Stokes/Darcy model

    Jia, Xiaofeng | Li, Jichun | Jia, Hongen

    Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 1 P.267

    https://doi.org/10.1002/num.22300 [Citations: 7]
  4. Numerical Analysis of a BDF2 Modular Grad-Div Stability Method for the Stokes/Darcy Equations

    Wang, Jiangshan | Meng, Lingxiong | Jia, Xiaofeng | Jia, Hongen

    Acta Mathematica Scientia, Vol. 42 (2022), Iss. 5 P.1981

    https://doi.org/10.1007/s10473-022-0515-z [Citations: 1]
  5. Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model

    Wang, Jiangshan | Meng, Lingxiong | Jia, Hongen

    Electronic Research Archive, Vol. 28 (2020), Iss. 3 P.1191

    https://doi.org/10.3934/era.2020065 [Citations: 0]
  6. On the solution of the steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition

    Yang, Di | He, Yinnian | Cao, Luling

    Journal of Mathematical Analysis and Applications, Vol. 505 (2022), Iss. 1 P.125577

    https://doi.org/10.1016/j.jmaa.2021.125577 [Citations: 2]
  7. Decoupled modified characteristic FEMs for fully evolutionary Navier–Stokes–Darcy model with the Beavers–Joseph interface condition

    Cao, Luling | He, Yinnian | Li, Jian | Yang, Di

    Journal of Computational and Applied Mathematics, Vol. 383 (2021), Iss. P.113128

    https://doi.org/10.1016/j.cam.2020.113128 [Citations: 11]