Geodesic
Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 1, pp. 47-59 
I. A. Blatov; E. V. Kitaeva. Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 1, pp. 47-59. http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a5/
@article{SJVM_2016_19_1_a5,
     author = {I. A. Blatov and E. V. Kitaeva},
     title = {Convergence of the adapting grid method of {Bakhvalov's} type for singularly perturbed boundary value problems},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {47--59},
     year = {2016},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a5/}
}
TY  - JOUR
AU  - I. A. Blatov
AU  - E. V. Kitaeva
TI  - Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2016
SP  - 47
EP  - 59
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a5/
LA  - ru
ID  - SJVM_2016_19_1_a5
ER  - 
%0 Journal Article
%A I. A. Blatov
%A E. V. Kitaeva
%T Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2016
%P 47-59
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a5/
%G ru
%F SJVM_2016_19_1_a5

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

We consider the Galerkin finite element method for non-self-adjoint boundary value problems on Bakhvalov's grids. Using the Galerkin projections method the convergence of a sequence of computational grids with an unknown boundary of the boundary layer has been proved. Numerical examples are presented.

[1] Natterer F., “Uniform convergence of Galerkin method for splines on highly nonuniform meshes”, Math. Comput., 31 (1977), 457–468 | MR | Zbl

[2] Blatov I. A., Strygin V. V., “On best possible order of convergence estimates in the collocation method and Galerkin's method for singularly perturbed boundary value problems for systems of first order ordinary differential equations”, Math. Comput., 68 (1999), 683–715 | DOI | MR | Zbl

[3] Liseikin V. D., Grid Generation Methods, Springer-Verlag, Berlin, 1999 | MR | Zbl

[4] Gil'manov A. N., Metody adaptivnykh setok v zadachakh gazovoy dinamiki, Nauka, FIZMATLIT, M., 2000 | MR

[5] Shishkin G. I., “Setochnaya approksimatsiya singulyarno vozmushchennykh kraevykh zadach na lokal'no pereizmel'chaemykh setkakh. Uravnenie konvektsii-diffuzii”, Zhurn. vychisl. matem. i mat. fiziki, 40:5 (2000), 714–725 | MR | Zbl

[6] Shishkin G. I., “Setochnaya approksimatsiya parabolicheskikh uravneniy konvektsii-diffuzii na apriorno adaptiruyushchikhsya setkakh; ravnomerno skhodyashchiesya skhemy”, Zhurn. vychisl. matem. i mat. fiziki, 48:6 (2008), 1014–1033 | MR | Zbl

[7] Blatov I. A., Dobrobog N. V., “Uslovnaya ravnomernaya skhodimost' algoritmov adaptatsii v metode konechnykh elementov dlya singulyarno vozmushchennykh zadach”, Zhurn. vychisl. matem. i mat. fiziki, 50:9 (2010), 1550–1568 | MR | Zbl

[8] Blatov I. A., “O proektsionnom metode dlya singulyarno vozmushchennykh kraevykh zadach”, Zhurn. vychisl. matem. i mat. fiziki, 30:7 (1990), 1031–1044 | MR | Zbl

[9] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zhurn. vychisl. matem. i mat. fiziki, 9:4 (1969), 841–859 | MR | Zbl

[10] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR

[11] Vasil'eva A. B., Butuzov V. F., Asimptoticheskoe razlozhenie resheniy singulyarno vozmushchennykh uravneniy, Nauka, M., 1973 | MR