Inf-sup condition for the 3-D P2-iso-P1 Taylor-Hood finite element; application to Maxwell equations

Partrick Ciarlet; Vivette Girault

doi:10.1016/S1631-073X(02)02564-5

Inf-sup condition for the 3-D P₂-iso-P₁ Taylor-Hood finite element; application to Maxwell equations

Partrick Ciarlet
, Vivette Girault

UPMC Université de Paris VI

Research output: Contribution to journal › Article › peer-review

Abstract

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].

Translated title of the contribution	Condition inf-sup pour l'élément fini de Taylor-Hood P₂-iso-P-₁, 3-D; application aux équations de Maxwell
Original language	English
Pages (from-to)	827-832
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	335
Issue number	10
DOIs	https://doi.org/10.1016/S1631-073X(02)02564-5
Publication status	Published - 15 Nov 2002

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title = "Inf-sup condition for the 3-D P2-iso-P1 Taylor-Hood finite element; application to Maxwell equations",

abstract = "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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AU - Girault, Vivette

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N2 - 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].

AB - 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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DO - 10.1016/S1631-073X(02)02564-5

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SN - 1631-073X

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IS - 10

ER -

Inf-sup condition for the 3-D P2-iso-P1 Taylor-Hood finite element; application to Maxwell equations

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Inf-sup condition for the 3-D P₂-iso-P₁ Taylor-Hood finite element; application to Maxwell equations