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Coupling Harmonic Functions-Finite Elements for Solving the Stream Function-Vorticity Stokes Problem

Abboud, Toufic and Salaün, Michel and Salmon, Stéphanie Coupling Harmonic Functions-Finite Elements for Solving the Stream Function-Vorticity Stokes Problem. (2004) Numerical Methods for Partial Differential Equations, 20 (5). 765-788. ISSN 0749-159X

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/num.20005/references

Abstract

We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity form. The classical finite element method of degree one usually used does not allow the vorticity on the boundary of the domain to be computed satisfactorily when the meshes are unstructured and does not converge optimally. To better approach the vorticity along the boundary, we propose that harmonic functions obtained by integral representation be used. Numerical results are very satisfactory, and we prove that this new numerical scheme leads to an optimal convergence rate of order 1 for the natural norm of the vorticity and, under higher regularity assumptions, from 3/2 to 2 for the quadratic norm of the vorticity.

Item Type:Article
Additional Information:Thanks to John Wiley editor. The definitive version is available at http://onlinelibrary.wiley.com. The original PDF of the article can be found at Numerical Methods for Partial Differential Equations web site : http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291098-2426
HAL Id:hal-00815176
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Conservatoire National des Arts et Métiers - CNAM (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Université Louis Pasteur-Strasbourg I - ULP (FRANCE)
Other partners > Ecole Polytechnique (FRANCE)
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Deposited By: Michel Salaun
Deposited On:18 Apr 2013 09:58

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