Comptes Rendus
Numerical Analysis
A new approach for approximating linear elasticity problems
Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 351-356.

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.

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.

Accepted:
Published online:
DOI: 10.1016/j.crma.2008.01.014
Philippe G. Ciarlet 1; Patrick Ciarlet 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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Philippe G. Ciarlet; Patrick Ciarlet. A new approach for approximating linear elasticity problems. Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 351-356. doi : 10.1016/j.crma.2008.01.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.01.014/

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

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

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

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

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

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

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