## Abstract

We study a hybridizable discontinuous Galerkin method for solving the vorticity-velocity formulation of the Stokes equations in three-space dimensions. We show how to hybridize the method to avoid the construction of the divergence-free approximate velocity spaces, recover an approximation for the pressure and implement the method efficiently. We prove that, when all the unknowns use polynomials of degree k≥0, the L ^{2} norm of the errors in the approximate vorticity and pressure converge with order k+1/2 and the error in the approximate velocity converges with order k+1. We achieve this by letting the normal stabilization function go to infinity in the error estimates previously obtained for a hybridizable discontinuous Galerkin method.

Original language | English (US) |
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Pages (from-to) | 256-270 |

Number of pages | 15 |

Journal | Journal of Scientific Computing |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2012 |

### Bibliographical note

Funding Information:The first author was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute.

## Keywords

- Discontinuous Galerkin methods
- Hybridization
- Incompressible fluid flow