Fairag, Faisal (1998) *A two-level finite-element discretization of the stream function form of the Navier-Stokes equations.* Comput. Math. Appl., 36 (2). pp. 117-127.

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## Abstract

We analyze a two-level method of discretizing the stream function form of the Navier-Stokes equations. This report presents the two-level algorithm and error analysis for the case of conforming elements. The two-level algorithm consists of solving a small nonlinear system on the coarse mesh, then solving a linear system on the fine mesh. The basic result states that the error between the coarse and fine meshes are related superlinearly via $|\psi- \psi^h|_2\le C\left\{ \inf_{w^h\in X^h}|\psi- w^h|_2+ |\ln h|^{1/2}\cdot|\psi- \psi^H|_1\right\}$. As an example, if the Clough-Tocher triangles or the Bogner-Fox-Schmit rectangles are used, then the coarse and fine meshes are related by $h= O(H^{3/2}|\ln H|^{1/4})$.

Item Type: | Article |
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Uncontrolled Keywords: | Naviex-Stokes equations, Reynolds number, Finite element, Two-level methods, Stream function formulation. |

Date: | 1998 |

Date Type: | Publication |

Subjects: | Math |

Divisions: | College Of Sciences > Mathematical Science Dept |

Creators: | Fairag, Faisal |

Email: | ffairag@kfupm.edu.sa |

ID Code: | 1250 |

Deposited By: | FAISAL ABDULKARIM M FAIRAG |

Deposited On: | 05 May 2008 12:07 |

Last Modified: | 12 Apr 2011 13:08 |

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