## Abstract

In this paper we analyze the L^{2} least-squares finite element method for a stationary velocity-vorticity problem arising in incompressible inviscid rotational flows. Introducing the additional vorticity variable, we rewrite the governing equations of incompressible inviscid rotational flow in the velocity-vorticity-pressure formulation and then further split the formulation into the pressure and velocity-vorticity subsystems. After time-discretizing the time derivative and linearizing the non-linear terms, we reach the stationary velocity-vorticity system. The L^{2} least-squares finite element approach is applied to generate accurate numerical solutions of the velocity-vorticity system with suitable boundary conditions. We show that this approach produces an optimal rate of convergence in the H^{1} norm for velocity and suboptimal rate in the L^{2} norm for vorticity. A numerical example is given which confirms the theoretical results.

Original language | English |
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Pages (from-to) | 604-613 |

Number of pages | 10 |

Journal | Applied Mathematics and Computation |

Volume | 185 |

Issue number | 1 |

DOIs | |

State | Published - 1 Feb 2007 |

## Keywords

- Finite element methods
- Incompressible inviscid rotational flows
- Least squares

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