Volume 6, Issue 1
Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model

East Asian J. Appl. Math., 6 (2016), pp. 60-79.

Published online: 2018-02

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• 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.

• Keywords

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

65N15, 65N30, 76D07

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• RIS
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@Article{EAJAM-6-60, author = {}, title = {Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080215.111215a}, url = {http://global-sci.org/intro/article_detail/eajam/10773.html} }
TY - JOUR T1 - Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model JO - East Asian Journal on Applied Mathematics VL - 1 SP - 60 EP - 79 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.080215.111215a UR - https://global-sci.org/intro/article_detail/eajam/10773.html KW - Navier-Stokes equations, Darcy’s law, multimodeling problems, two-grid method. AB -

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.

Jing Zhao & Tong Zhang. (2020). Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model. East Asian Journal on Applied Mathematics. 6 (1). 60-79. doi:10.4208/eajam.080215.111215a
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