Volume 1, Issue 6
Improved Local Projection for the Generalized Stokes Problem

Kamel Nafa

Adv. Appl. Math. Mech., 1 (2009), pp. 862-873.

Published online: 2009-01

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  • Abstract

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although the stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This makes it much simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.

  • Keywords

Generalized Stokes equations stabilized finite elements local projection convergence error estimates

  • AMS Subject Headings

65N12 65N30 65N15 76D07

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COPYRIGHT: © Global Science Press

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@Article{AAMM-1-862, author = {Kamel Nafa}, title = {Improved Local Projection for the Generalized Stokes Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {6}, pages = {862--873}, abstract = {

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although the stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This makes it much simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09S07}, url = {http://global-sci.org/intro/article_detail/aamm/8402.html} }
TY - JOUR T1 - Improved Local Projection for the Generalized Stokes Problem AU - Kamel Nafa JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 862 EP - 873 PY - 2009 DA - 2009/01 SN - 1 DO - http://dor.org/10.4208/aamm.09-m09S07 UR - https://global-sci.org/intro/aamm/8402.html KW - Generalized Stokes equations KW - stabilized finite elements KW - local projection KW - convergence KW - error estimates AB -

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although the stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This makes it much simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.

Kamel Nafa. (1970). Improved Local Projection for the Generalized Stokes Problem. Advances in Applied Mathematics and Mechanics. 1 (6). 862-873. doi:10.4208/aamm.09-m09S07
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