On considère la discrétisation des équations de Maxwell, telle qu'elle a été proposée dans [3,2,1]. Les approximations numériques du champ électromagnétique et du multiplicateur de Lagrange associé à la divergence du champ sont réalisées à l'aide de l'élément fini de Taylor–Hood P2-iso-P1, et complétées de fonctions-test singulières, lorsque le domaine de calcul est non convexe, à bord non régulier. Le but de la Note est de prouver l'existence d'une condition inf-sup discrète. On peut également appliquer ce résultat à la discrétisation du système de Stokes en vitesse-pression [7].
We consider the discretization of Maxwell equations, proposed in [3,2,1]. The electromagnetic field and the Lagrange multiplier related to its divergence are approximated numerically by the P2-iso-P1 Taylor–Hood Finite Element. Singular test-functions are added when the domain is non-convex, with a non-smooth boundary. The aim of this Note is to establish a discrete inf-sup condition. The result can be applied to the discretization of the velocity-pressure Stokes system [7].
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Patrick Ciarlet 1 ; Vivette Girault 2
@article{CRMATH_2002__335_10_827_0,
author = {Patrick Ciarlet and Vivette Girault},
title = {Condition \protect\emph{inf-sup} pour l'\'el\'ement fini de {Taylor{\textendash}Hood} {<strong>\protect\emph{P}\protect\textsubscript{2}</strong>-iso-<strong>\protect\emph{P}\protect\textsubscript{1}</strong>,} {3-D} ; application aux \'equations de {Maxwell}},
journal = {Comptes Rendus. Math\'ematique},
pages = {827--832},
publisher = {Elsevier},
volume = {335},
number = {10},
year = {2002},
doi = {10.1016/S1631-073X(02)02564-5},
language = {fr},
}
TY - JOUR AU - Patrick Ciarlet AU - Vivette Girault TI - Condition inf-sup pour l'élément fini de Taylor–Hood P2-iso-P1, 3-D ; application aux équations de Maxwell JO - Comptes Rendus. Mathématique PY - 2002 SP - 827 EP - 832 VL - 335 IS - 10 PB - Elsevier DO - 10.1016/S1631-073X(02)02564-5 LA - fr ID - CRMATH_2002__335_10_827_0 ER -
%0 Journal Article %A Patrick Ciarlet %A Vivette Girault %T Condition inf-sup pour l'élément fini de Taylor–Hood P2-iso-P1, 3-D ; application aux équations de Maxwell %J Comptes Rendus. Mathématique %D 2002 %P 827-832 %V 335 %N 10 %I Elsevier %R 10.1016/S1631-073X(02)02564-5 %G fr %F CRMATH_2002__335_10_827_0
Patrick Ciarlet; Vivette Girault. Condition inf-sup pour l'élément fini de Taylor–Hood P2-iso-P1, 3-D ; application aux équations de Maxwell. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 827-832. doi : 10.1016/S1631-073X(02)02564-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02564-5/
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