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A two-level finite-element discretization of the stream function form of the Navier-Stokes equations

✍ Scribed by F. Fairag

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 588 KB
Volume: 36
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(98)00123-0

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✦ Synopsis

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 eltements. 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:

As an example, if the Clough-Tocher triangles or the Bogner-Fox-Schmit rectangles are used, then the coarse aJld fine meshes are related by h = O(H3/211nHI1/4 ).

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