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Vector potentials in three‐dimensional non‐smooth domains
Author(s) -
Amrouche C.,
Bernardi C.,
Dauge M.,
Girault V.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199806)21:9<823::aid-mma976>3.0.co;2-b
Subject(s) - mathematics , uniqueness , discretization , domain (mathematical analysis) , divergence (linguistics) , convergence (economics) , mathematical analysis , humanities , philosophy , linguistics , economics , economic growth
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.