Geodesic
Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 223-234.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the rate of convergence of the semidiscrete Galerkin method for linear hyperbolic equations in a Hilbert space. We establish asymptotic estimates for the error arising as a result of the arbitrariness in the choice of subspaces in which the approximation problems are solved. 
@article{MZM_2001_69_2_a6,
     author = {S. E. Zhelezovsky},
     title = {Estimates for the {Rate} of {Convergence} of the {Galerkin} {Method} for {Abstract} {Hyperbolic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {223--234},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a6/}
}
TY  - JOUR
AU  - S. E. Zhelezovsky
TI  - Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations
JO  - Matematičeskie zametki
PY  - 2001
SP  - 223
EP  - 234
VL  - 69
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a6/
LA  - ru
ID  - MZM_2001_69_2_a6
ER  - 
%0 Journal Article
%A S. E. Zhelezovsky
%T Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations
%J Matematičeskie zametki
%D 2001
%P 223-234
%V 69
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a6/
%G ru
%F MZM_2001_69_2_a6
S. E. Zhelezovsky. Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 223-234. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a6/

[1] Smagin V. V., “Otsenki pogreshnosti poludiskretnykh priblizhenii po Galerkinu dlya parabolicheskikh uravnenii s kraevym usloviem tipa Neimana”, Izv. vuzov. Matem., 1996, no. 3, 50–57 | MR | Zbl

[2] Smagin V. V., “Otsenki skorosti skhodimosti proektsionnogo i proektsionnoraznostnogo metodov dlya slabo razreshimykh parabolicheskikh uravnenii”, Matem. sb., 188:3 (1997), 143–160 | MR

[3] Zhelezovskaya L. A., Zhelezovskii S. E., Kirichenko V. F., Krysko V. A., “O skorosti skhodimosti metoda Bubnova–Galerkina dlya giperbolicheskikh uravnenii”, Differents. uravneniya, 26:2 (1990), 323–333 | MR

[4] Zhelezovskii S. E., “Metod Bubnova–Galerkina dlya abstraktnoi kvazilineinoi zadachi o statsionarnom deistvii”, Differents. uravneniya, 31:7 (1995), 1222–1231 | MR | Zbl

[5] Zhelezovskii S. E., O skorosti skhodimosti metoda Galerkina dlya odnogo klassa kvazilineinykh evolyutsionnykh zadach, Dep. VINITI 08.01.98. No. 24–V98, Red. Sib. matem. zh., Novosibirsk, 1998

[6] Lyashko A. D., “O skhodimosti metodov tipa Galerkina”, Dokl. AN SSSR, 120:2 (1958), 242–244 | MR | Zbl

[7] Vainikko G. M., Oya P. E., “O skhodimosti i bystrote skhodimosti metoda Galerkina dlya abstraktnykh evolyutsionnykh uravnenii”, Differents. uravneniya, 11:7 (1975), 1269–1277 | MR | Zbl

[8] Sobolevskii P. E., “Teorema o smeshannykh proizvodnykh i otsenka skorosti skhodimosti metoda Galerkina dlya parabolicheskikh uravnenii”, Dokl. AN USSR. Ser. A, 1987, no. 8, 12–16 | MR | Zbl

[9] Zarubin A. G., “O skorosti skhodimosti metoda Faedo–Galerkina dlya kvazilineinykh nestatsionarnykh operatornykh uravnenii”, Differents. uravneniya, 26:12 (1990), 2051–2059 | MR | Zbl

[10] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972

[11] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967

[12] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973

[13] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981

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

[15] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978

[16] Bekkenbakh E., Bellman R., Neravenstva, Mir, M., 1965