Volume 1, Issue 2
An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations

Adv. Appl. Math. Mech., 1 (2009), pp. 273-287.

Published online: 2009-01

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• Abstract

In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.

• Keywords

stabilized finite element method, multiscale functions, Petrov-Galerkin approach, inf-sup condition.

76D05, 65N30, 35K60

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@Article{AAMM-1-273, author = {Zhihao and Ge and and 20626 and and Zhihao Ge and Yinnian and He and and 20627 and and Yinnian He and Lingyu and Song and and 20628 and and Lingyu Song}, title = {An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {273--287}, abstract = {

In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8369.html} }
TY - JOUR T1 - An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations AU - Ge , Zhihao AU - He , Yinnian AU - Song , Lingyu JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 273 EP - 287 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8369.html KW - stabilized finite element method, multiscale functions, Petrov-Galerkin approach, inf-sup condition. AB -

In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.

Zhihao Ge, Yinnian He & Lingyu Song. (1970). An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations. Advances in Applied Mathematics and Mechanics. 1 (2). 273-287. doi:
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