## Abstract

This paper is devoted to the error analysis of least-squares finite element approximations to the stationary incompressible Oseen type equations with the homogeneous velocity boundary condition. With the vorticity as a new dependent variable, we consider two first-order system problems for the Oseen type equations in the velocityvorticity-pressure and the velocity-vorticity-Bernoulli pressure formulations. The least-squares functional is defined in terms of the sum of the squared H^{-1} and L^{2} norms of the residual equations over a suitable product function space. The well-posedness of the proposed least-squares variational problem is shown. We then analyze the case where the H^{-1} norm in the least-squares functional is replaced by a discrete functional to make the computation feasible. Optimal error estimates for all unknowns are derived.

Original language | English |
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Pages (from-to) | 77-88 |

Number of pages | 12 |

Journal | Applied Numerical Mathematics |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2005 |

## Keywords

- Finite element methods
- First-order system least squares
- Navier-Stokes equations
- Oseen type equations
- Velocity-vorticity-Bernoulli pressure formulation
- Velocity-vorticity-pressure formulation

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