### 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.

Original language | English |
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Pages (from-to) | 862-873 |

Number of pages | 12 |

Journal | Advances in Applied Mathematics and Mechanics |

Volume | 1 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Convergence
- Error estimates
- Generalized stokes equations
- Local projection
- Stabilized finite elements

### ASJC Scopus subject areas

- Applied Mathematics
- Mechanical Engineering

### Cite this

**Improved local projection for the generalized stokes problem.** / Nafa, Kamel.

Research output: Contribution to journal › Article

*Advances in Applied Mathematics and Mechanics*, vol. 1, no. 6, pp. 862-873. https://doi.org/10.4208/aamm.09-m09S07

}

TY - JOUR

T1 - Improved local projection for the generalized stokes problem

AU - Nafa, Kamel

PY - 2009

Y1 - 2009

N2 - 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.

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.

KW - Convergence

KW - Error estimates

KW - Generalized stokes equations

KW - Local projection

KW - Stabilized finite elements

UR - http://www.scopus.com/inward/record.url?scp=84863498739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863498739&partnerID=8YFLogxK

U2 - 10.4208/aamm.09-m09S07

DO - 10.4208/aamm.09-m09S07

M3 - Article

AN - SCOPUS:84863498739

VL - 1

SP - 862

EP - 873

JO - Advances in Applied Mathematics and Mechanics

JF - Advances in Applied Mathematics and Mechanics

SN - 2070-0733

IS - 6

ER -