Geodesic
Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 908-922 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An implicit projection-difference scheme is constructed for the nonstationary Stokes equation in cylindrical coordinates. No axial symmetry is assumed. Under minimal assumptions about the initial data, convergence rate estimates are obtained that are uniform in the inner radius of the domain of order $(\tau^{1/2}+h)^\alpha$, $\alpha=1$, $2$. The results remain valid for domains with no hole and in the case of Cartesian coordinates. 
@article{ZVMMF_2010_50_5_a9,
     author = {E. I. Aksenova},
     title = {Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {908--922},
     year = {2010},
     volume = {50},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a9/}
}
TY  - JOUR
AU  - E. I. Aksenova
TI  - Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 908
EP  - 922
VL  - 50
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a9/
LA  - ru
ID  - ZVMMF_2010_50_5_a9
ER  - 
%0 Journal Article
%A E. I. Aksenova
%T Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 908-922
%V 50
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a9/
%G ru
%F ZVMMF_2010_50_5_a9
E. I. Aksenova. Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 908-922. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a9/

[1] Temam R., Uravneniya Nave-Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[2] Ladyzhenskaya O. A., “Ob odnoznachnoi razreshimosti v tselom trekhmernoi zadachi Koshi dlya uravnenii Nave–Stoksa pri nalichii osevoi simmetrii”, Zap. nauchn. seminara LOMI, 7, 1968, 155–177 | Zbl

[3] Ladyzhenskaya O. A., Rivkind V. I., “O metode peremennykh napravlenii dlya rascheta techenii vyazkoi neszhimaemoi zhidkosti v tsilindricheskikh koordinatakh”, Izv. AN SSSR, 35 (1971), 259–268 | MR | Zbl

[4] Rivkind V. I., Epshtein B. S., “Proektsionno-setochnye skhemy dlya reshenii uravnenii Nave–Stoksa v ortogonalnykh krivolineinykh sistemakh koordinat”, Vestn. LGU, 3:13 (1974), 53–56 | MR

[5] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl

[6] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[7] Varga R., Funktsionalnyi analiz i teoriya approksimatsii v chislennom analize, Mir, M., 1974 | MR | Zbl

[8] Bykova E. I., “Otsenki skorosti skhodimosti proektsionno-raznostnykh skhem dlya parabolicheskikh uravnenii v oblasti s malym otverstiem”, Zh. vychisl. matem. i matem. fiz., 24:11 (1984), 1694–1703 | MR | Zbl

[9] Zlotnik A. A., Proektsionno-raznostnye skhemy dlya nestatsionarnykh zadach s negladkimi dannymi, Dis. ...kand. fiz.-matem. nauk, MGU, M., 1979

[10] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR