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Vector potentials in three-dimensional non-smooth domains

✍ Scribed by C. Amrouche; C. Bernardi; M. Dauge; V. Girault

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
294 KB
Volume
21
Category
Article
ISSN
0170-4214

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✦ Synopsis

This paper presents several results concerning the vector potential which can be associated with a divergence-free function in a bounded three-dimensional domain. Different types of boundary conditions are given, for which the existence, uniqueness and regularity of the potential are studied. This is applied firstly to the finite element discretization of these potentials and secondly to a new formulation of incompressible viscous flow problems.

On pre´sente dans cet article un certain nombre de re´sultats concernant le potentiel vecteur associe´aune fonction adivergence nulle dans un ouvert borne´de dimension trois. En particulier, plusieurs types de conditions aux limites sont propose´s, pour lesquels on discute l'existence, l'unicite´et la re´gularite´du potentiel vecteur. On analyse la convergence d'une discre´tisation par e´le´ments finis de ces potentiels et on indique une application concernant l'approximation de fluides visqueux incompressibles. 1998

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