Geodesic
Finite element method for non-selfadjoint spectral problems
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 4, pp. 51-62 
S. I. Solov'ev. Finite element method for non-selfadjoint spectral problems. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 4, pp. 51-62. http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a4/
@article{UZKU_2006_148_4_a4,
     author = {S. I. Solov'ev},
     title = {Finite element method for non-selfadjoint spectral problems},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {51--62},
     year = {2006},
     volume = {148},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a4/}
}
TY  - JOUR
AU  - S. I. Solov'ev
TI  - Finite element method for non-selfadjoint spectral problems
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2006
SP  - 51
EP  - 62
VL  - 148
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a4/
LA  - ru
ID  - UZKU_2006_148_4_a4
ER  - 
%0 Journal Article
%A S. I. Solov'ev
%T Finite element method for non-selfadjoint spectral problems
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2006
%P 51-62
%V 148
%N 4
%U http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a4/
%G ru
%F UZKU_2006_148_4_a4

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

The finite element method with numerical integration for a differential eigenvalue problem of second order for non-selfadjoint operator is investigated. Error estimates for approximate eigenvalues and generalized eigensubspaces are obtained.

[1] Vainikko G. M., “O bystrote skhodimosti priblizhennykh metodov v probleme sobstvennykh znachenii”, Zhurn. vychisl. matem. i matem. fiz., 7:5 (1967), 977–987 | MR

[2] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969, 456 pp. | MR

[3] Fix G. J., “Effects of quadrature errors in finite element approximation of steady state, eigenvalue and parabolic problems”, The mathematical foundations of the finite element method with applications to partial differential equations, ed. Aziz A. K., Academic Press, N. Y., 1972, 525–556 | MR

[4] Solovëv S. I., “Issledovanie tochnosti setochnykh skhem MKE s chislennym integrirovaniem dlya zadachi na sobstvennye znacheniya”, Primenenie informatiki i vychisl. tekhniki pri reshenii narodnokhoz. zadach, Tez. dokl. Respubl. konf., Minsk, 1989, 127–128

[5] Solovëv S. I., Metod konechnykh elementov dlya simmetrichnykh zadach na sobstvennye znacheniya s nelineinym vkhozhdeniem parametra, Dis. $\ldots$ kand. fiz.-mat. nauk, Kazan. gos. un-t, Kazan, 1990

[6] Solovëv S. I., “Pogreshnost metoda Bubnova–Galerkina s vozmuscheniyami dlya simmetrichnykh spektralnykh zadach s nelineinym vkhozhdeniem parametra”, Zhurn. vychisl. matem. i matem. fiz., 32:5 (1992), 675–691 | MR

[7] Solovëv S. I., “Superskhodimost konechno-elementnykh approksimatsii sobstvennykh funktsii”, Differents. uravneniya, 30:7 (1994), 1230–1238 | MR

[8] Solovëv S. I., “Superskhodimost konechno-elementnykh approksimatsii sobstvennykh podprostranstv”, Differents. uravneniya, 38:5 (2002), 710–711 | MR

[9] Banerjee U., Osborn J. E., “Estimation of the effect of numerical integration in finite element eigenvalue approximation”, Numer. Math., 56 (1990), 735–762 | DOI | MR | Zbl

[10] Osborn J. E., “Spectral approximation for compact operators”, Math. Comp., 26 (1975), 712–725 | DOI | MR

[11] Babuška I., Osborn J. E., “Eigenvalue problems”, Handbook of numerical analysis, v. II, Finite element methods, eds. Ciarlet P. G., Lions J. L., North-Holland, Amsterdam, 1991, 642–787 | MR

[12] Kolata W., “Approximation of variationally posed eigenvalue problems”, Numer. Math., 29 (1978), 159–171 | DOI | MR | Zbl

[13] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972, 740 pp. | MR | Zbl

[14] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980, 512 pp. | MR