## Abstract

In this article we analyze the L^{2} least-squares finite element approximations to the incompressible inviscid rotational flow problem, which is recast into the velocity-vorticity-pressure formulation. The least-squares functional is defined in terms of the sum of the squared L^{2} norms of the residual equations over a suitable product function space. We first derive a coercivity type a priori estimate for the first-order system problem that will play the crucial role in the error analysis. We then show that the method exhibits an optimal rate of convergence in the H^{1} norm for velocity and pressure and a suboptimal rate of convergence in the L^{2} norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates.

Original language | English |
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Pages (from-to) | 831-842 |

Number of pages | 12 |

Journal | Numerical Methods for Partial Differential Equations |

Volume | 20 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2004 |

## Keywords

- Euler equations
- Incompressible inviscid rotational flows
- Least-squares finite element methods
- Standing vortex problems
- Velocity-vorticity-pressure formulation