Approximation of the arch problem by residual-free bubbles
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 2, pp. 271-293.

On considère un problème de déplacement d'une arche chargée et de faible épaisseur. Pour approcher la solution de ce problème, on donne une méthode d'éléments finis Galerkin mixte conforme qui tient compte d'une approximation de la forme de l'arche. Cependant une application directe d'une telle méthode ne donne pas de résultat de convergence satisfaisant pour une faible épaisseur. On propose d'enrichir cette méthode par des fonctions bulles résiduelles.

We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, a conforming mixed finite element method which takes into account an approximation of the middle line of the arch is given. But for a very small thickness such a method gives poor error bounds. the conforming Galerkin method is then enriched with residual-free bubble functions.

Classification : 65N12
Mots-clés : mixed method, Lagrange multipliers, conforming approximations, residual-free-bubble 
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Agouzal, A.; El Alami El Ferricha, M. Approximation of the arch problem by residual-free bubbles. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 2, pp. 271-293. http://www.numdam.org/item/M2AN_2001__35_2_271_0/

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