Geodesic
Approximation of the arch problem by residual-free bubbles
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 271-293

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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.

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.

Classification : 65N12
Keywords: mixed method, Lagrange multipliers, conforming approximations, residual-free-bubble 
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     title = {Approximation of the arch problem by residual-free bubbles},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {271--293},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {2},
     year = {2001},
     mrnumber = {1825699},
     zbl = {1007.74070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_271_0/}
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Agouzal, A.; El Alami El Ferricha, M. Approximation of the arch problem by residual-free bubbles. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 271-293. http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_271_0/