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

Zhihao Ge, Yinnian He & Lingyu Song

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.

  • AMS Subject Headings

76D05, 65N30, 35K60

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{AAMM-1-273, author = {Ge , ZhihaoHe , Yinnian and Song , Lingyu}, 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.

Ge , ZhihaoHe , Yinnian and Song , Lingyu. (2009). 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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