Numerical Analysis
Gradient-prolongation commutativity and graph theory

Presented by: Philippe G. Ciarlet

Musy, François1; Nicolas, Laurent2; Perrussel, Ronan1, 2
1 Institut Camille Jordan, École Centrale de Lyon, 69134 Ecully cedex, France
2 Centre de génie électrique de Lyon, École Centrale de Lyon, 69134 Ecully cedex, France
Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 707-712.

This Note gives conditions that must be imposed to algebraic multilevel discretizations involving at the same time nodal and edge elements so that a gradient-prolongation commutativity condition will be satisfied; this condition is very important, since it characterizes the gradients of coarse nodal functions in the coarse edge function space. They will be expressed using graph theory and they provide techniques to compute approximation bases at each level.

Cette Note donne des conditions qui doivent être imposées aux discrétisations multiniveau algébriques en éléments finis nodaux et d'arête de façon à assurer la commutativité entre gradient et prolongement ; cette relation importante caractérise les gradients des fonctions nodales grossières dans l'espace des fonctions d'arête grossières. Ces conditions seront exprimées en terme de graphes et elles permettent d'introduire des méthodes de calcul des bases d'approximation aux différents niveaux.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.09.037
Musy, François 1; Nicolas, Laurent 2; Perrussel, Ronan 1, 2

1 Institut Camille Jordan, École Centrale de Lyon, 69134 Ecully cedex, France
2 Centre de génie électrique de Lyon, École Centrale de Lyon, 69134 Ecully cedex, France 
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Musy, François; Nicolas, Laurent; Perrussel, Ronan. Gradient-prolongation commutativity and graph theory. Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 707-712. doi : 10.1016/j.crma.2005.09.037. https://www.numdam.org/articles/10.1016/j.crma.2005.09.037/

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