We explain how to derive a network element for the linear elasticity problem. After presenting sufficient conditions on the network for the validity of a discrete Korn inequality, we also propose several variations of the presented method and in particular we explain how it can be used on meshes to derive schemes that remain stable while keeping the stencil as compact as possible. Numerical examples illustrate the good behavior of the method, in both the mesh-based and truly meshless contexts.
Nous expliquons comment contruire une méthode « éléments de réseau » pour le problème de l’élasticité linéaire. Après avoir présenté des conditions suffisantes sur le réseau de discrétisation pour qu’une inégalité de Korn discrète soit satisfaite, nous détaillons plusieurs variantes de la méthode proposée et en particulier nous expliquons comment elle permet aussi d’obtenir des schémas basés sur des maillages qui demeurent stables tout en maintenant le stencil aussi compact que possible. Nous illustrons le bon comportement de la méthode à la fois sur maillage et dans le cas complètement sans maillage.
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Mots-clés : Méthode sans maillage, Élasticité linéaire, Méthodes variationnelles
Julien Coatléven 1
CC-BY 4.0
@article{CRMECA_2023__351_S1_331_0,
author = {Julien Coatl\'even},
title = {Network element methods for linear elasticity},
journal = {Comptes Rendus. M\'ecanique},
pages = {331--356},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
number = {S1},
year = {2023},
doi = {10.5802/crmeca.231},
language = {en},
}
Julien Coatléven. Network element methods for linear elasticity. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023) no. S1, pp. 331-356. doi : 10.5802/crmeca.231. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.231/
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