Improved Local Projection for the Generalized Stokes Problem

Improved Local Projection for the Generalized Stokes Problem

Year:    2009

Author:    Kamel Nafa

Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.09-m09S07

Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 862–873

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Generalized Stokes equations stabilized finite elements local projection convergence error estimates.

Author Details

Kamel Nafa