no. 5-6
Numerical Analysis
A new approach for approximating linear elasticity problems
[Une nouvelle approche pour approcher les problèmes d'élasticité linéaire]

Présenté par : Robert Dautray

Ciarlet, Philippe G.1 ; Ciarlet, Patrick Jr.2
1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75015 Paris, France
Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 351-356.

Dans cette Note, nous présentons et analysons une nouvelle méthode d'approximation de problèmes d'élasticité linéaire en dimension deux ou trois. Cette approche fournit directement des approximations des déformations, c'est-à-dire sans approcher simultanément les déplacements, dans des espaces d'éléments finis où les conditions de compatibilité de Saint Venant sont exactement satisfaites dans un sens faible.

In this Note, we present and analyze a new method for approximating linear elasticity problems in dimension two or three. This approach directly provides approximate strains, i.e., without simultaneously approximating the displacements, in finite element spaces where the Saint Venant compatibility conditions are exactly satisfied in a weak form.

Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.01.014
Ciarlet, Philippe G. 1 ; Ciarlet, Patrick Jr. 2

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75015 Paris, France 
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Ciarlet, Philippe G.; Ciarlet, Patrick Jr. A new approach for approximating linear elasticity problems. Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 351-356. doi : 10.1016/j.crma.2008.01.014. http://www.numdam.org/articles/10.1016/j.crma.2008.01.014/

[1] Amrouche, C.; Ciarlet, P.G.; Gratie, L.; Kesavan, S. On the characterization of matrix fields as linearized strain tensor fields, J. Math. Pures Appl., Volume 86 (2006), pp. 116-132

[2] Arnold, D.N.; Falk, R.S.; Winther, R. Finite element exterior calculus, homological techniques, and applications, Acta Numer., Volume 15 (2006), pp. 1-155

[3] Arnold, D.N.; Winther, R. Mixed finite element methods for elasticity, Numer. Math., Volume 92 (2002), pp. 401-419

[4] Ciarlet, P.G.; Ciarlet, P. Jr. Another approach to linearized elasticity and a new proof of Korn's inequality, Math. Models Methods Appl. Sci., Volume 15 (2005), pp. 259-271

[5] P.G. Ciarlet, P. Ciarlet Jr., Direct computation of stresses in linearized elasticity, Parts 1 and 2, in preparation

[6] P.G. Ciarlet, P. Ciarlet Jr., S. Sauter, Finite element methods for the Saint Venant approach in elasticity, in preparation

[7] Duvaut, G.; Lions, J.L.; Duvaut, G.; Lions, J.L. Les Inéquations en Mécanique et en Physique, Inequalities in Mechanics and Physics, Dunod, 1972 (English translation:, 1976, Springer-Verlag)

[8] Nédélec, J.C. Mixed finite elements in R3, Numer. Math., Volume 35 (1980), pp. 315-341

[9] Schwartz, L. Théorie des Distributions, Hermann, Paris, 1966

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