Comptes Rendus
no. 1-2
Numerical Analysis
Four closely related equilibrated flux reconstructions for nonconforming finite elements
[Quatre reconstructions très proches de flux équilibrés pour les éléments finis non conformes]

Présenté par : Olivier Pironneau

Alexandre Ern1 ; Martin Vohralík2
1 Université Paris-Est, CERMICS, École des Ponts ParisTech, 77455 Marne-la-Vallée, France
2 INRIA Paris-Rocquencourt, B.P. 105, 78153 Le Chesnay, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 77-80.

Nous étudions la méthode des éléments finis non conformes de Crouzeix et Raviart pour lʼéquation de Laplace. Nous introduisons quatre reconstructions équilibrées du flux, par prescription directe ou par une approximation mixte de problèmes locaux de Neumann, soit sur le maillage simplectique de départ, soit sur un maillage dual. Nous montrons que toutes ces reconstructions coïncident si le système dʼéquations linéaires associé est résolu exactement. Nous considérons enfin une solution algébrique inexacte, ajustons les reconstructions du flux et indiquons les différences entre les reconstructions.

We consider the Crouzeix–Raviart nonconforming finite element method for the Laplace equation. We present four equilibrated flux reconstructions, by direct prescription or by mixed approximation of local Neumann problems, either relying on the original simplicial mesh only or employing a dual mesh. We show that all these reconstructions coincide provided the underlying system of linear algebraic equations is solved exactly. We finally consider an inexact algebraic solve, adjust the flux reconstructions, and point out the differences.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.01.001
Alexandre Ern 1 ; Martin Vohralík 2

1 Université Paris-Est, CERMICS, École des Ponts ParisTech, 77455 Marne-la-Vallée, France
2 INRIA Paris-Rocquencourt, B.P. 105, 78153 Le Chesnay, France 
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Alexandre Ern; Martin Vohralík. Four closely related equilibrated flux reconstructions for nonconforming finite elements. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 77-80. doi : 10.1016/j.crma.2013.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.001/

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Cité par Sources :

☆ This work was partly supported by the Groupement MoMaS (PACEN/CNRS, ANDRA, BRGM, CEA, EdF, IRSN) and by the ERT project “Enhanced oil recovery and geological sequestration of CO2: mesh adaptivity, a posteriori error control, and other advanced techniques” (LJLL UPMC/IFPEN).

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