Geodesic
An approximation by finite elements of the eigenvalue problem for degenerate differential operator
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 147 (2005) no. 3, pp. 157-165 
M. R. Timerbaev. An approximation by finite elements of the eigenvalue problem for degenerate differential operator. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 147 (2005) no. 3, pp. 157-165. http://geodesic.mathdoc.fr/item/UZKU_2005_147_3_a10/
@article{UZKU_2005_147_3_a10,
     author = {M. R. Timerbaev},
     title = {An approximation by finite elements of the eigenvalue problem for degenerate differential operator},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {157--165},
     year = {2005},
     volume = {147},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2005_147_3_a10/}
}
TY  - JOUR
AU  - M. R. Timerbaev
TI  - An approximation by finite elements of the eigenvalue problem for degenerate differential operator
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2005
SP  - 157
EP  - 165
VL  - 147
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2005_147_3_a10/
LA  - ru
ID  - UZKU_2005_147_3_a10
ER  - 
%0 Journal Article
%A M. R. Timerbaev
%T An approximation by finite elements of the eigenvalue problem for degenerate differential operator
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2005
%P 157-165
%V 147
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2005_147_3_a10/
%G ru
%F UZKU_2005_147_3_a10

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Eigenvalue problem for degenerate differential operator is considered. A discretization scheme based on multiplicative decomposition of singularity with special basis is constructed and its error approximation in energy norm is obtained.

[1] Chatelin F., Spectral Approximations of Linear Operators, Academic Press, N. Y., 1983 | MR | Zbl

[2] Babuska I., Osborn J. E., “Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems”, Math. Comp., 52 (1989), 275–297 | MR | Zbl

[3] Babuska I., Osborn J. E., “Eigenvalue problems”, Handbook of Numerical Analysis, Part 1, v. II, Finite Element Methods, Elsevier, 1991, 641–792 | DOI | MR

[4] Timerbaev M. R., “Multiplikativnoe vydelenie osobennosti v skhemakh MKE dlya ellipticheskikh vyrozhdayuschikhsya uravnenii”, Diff. uravneniya, 52:7 (2000), 1086–1093 | MR

[5] Khardi G., Littlvud Dzh. E., Polia G., Neravenstva, IL, M., 1948, 456 pp.

[6] Tribel Kh., Teoriya interpolyatsii. Funktsionalnye prostranstva. Differentsialnye operatory, Mir, M., 1980, 664 pp. | MR

[7] Timerbaev M. R., “Vesovye otsenki resheniya zadachi Dirikhle s anizotropnym vyrozhdeniem na chasti granitsy”, Izv. vuzov. Matematika, 2003, no. 1, 60–73 | MR | Zbl

[8] Timerbaev M. R., “Otsenki pogreshnosti n-mernoi splain-interpolyatsii v vesovykh normakh”, Izv. vuzov. Matematika, 1992, no. 10, 54–60 | MR | Zbl

[9] Timerbaev M. R., “Konechnoelementnaya approksimatsiya v vesovykh prostranstvakh Soboleva”, Izv. vuzov. Matematika, 2000, no. 11, 76–84 | MR | Zbl