[Extensions autoadjointes d'opérateurs différentiels et application à l'optimisation de forme]
Two approaches are proposed for the modelling of problems with small geometrical defects. The first approach is based on the theory of self adjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and the variational formulation is established. For both approaches the accuracy estimates are derived. Finally, the spectral problems are considered and the error estimates for eigenvalues are given.
On propose deux approches permettant de modéliser des problèmes avec des singularités géométriques. La première approche repose sur des extensions autoadjointes d'opérateurs différentiels avec conditions asymptotiques. Dans la seconde approche, on introduit des espaces fonctionnels avec développements asymptotiques séparés puis on établit la formulation variationnelle. On obtient des estimations montrant que la même précision est atteinte pour ces deux approches. Enfin, on considère des problèmes spectraux et on donne des estimations pour les valeurs propres.
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Mots-clés : Mécanique des solides numérique, Extensions autoadjointes, Formulation variationnelle, Estimations d'erreur
Serguei A. Nazarov 1 ; Jan Sokolowski 2
@article{CRMECA_2003__331_10_667_0, author = {Serguei A. Nazarov and Jan Sokolowski}, title = {Self adjoint extensions of differential operators in application to shape optimization}, journal = {Comptes Rendus. M\'ecanique}, pages = {667--672}, publisher = {Elsevier}, volume = {331}, number = {10}, year = {2003}, doi = {10.1016/j.crme.2003.07.003}, language = {en}, }
TY - JOUR AU - Serguei A. Nazarov AU - Jan Sokolowski TI - Self adjoint extensions of differential operators in application to shape optimization JO - Comptes Rendus. Mécanique PY - 2003 SP - 667 EP - 672 VL - 331 IS - 10 PB - Elsevier DO - 10.1016/j.crme.2003.07.003 LA - en ID - CRMECA_2003__331_10_667_0 ER -
Serguei A. Nazarov; Jan Sokolowski. Self adjoint extensions of differential operators in application to shape optimization. Comptes Rendus. Mécanique, Volume 331 (2003) no. 10, pp. 667-672. doi : 10.1016/j.crme.2003.07.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.07.003/
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