Geodesic
Piecewise-uniform grids, optimal with respect to the order of convergence, for singularly perturbed convection-diffusion equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2002), pp. 60-72.

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

@article{IVM_2002_3_a7,
     author = {G. I. Shishkin},
     title = {Piecewise-uniform grids, optimal with respect to the order of convergence, for singularly perturbed convection-diffusion equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--72},
     publisher = {mathdoc},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2002_3_a7/}
}
TY  - JOUR
AU  - G. I. Shishkin
TI  - Piecewise-uniform grids, optimal with respect to the order of convergence, for singularly perturbed convection-diffusion equations
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2002
SP  - 60
EP  - 72
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2002_3_a7/
LA  - ru
ID  - IVM_2002_3_a7
ER  - 
%0 Journal Article
%A G. I. Shishkin
%T Piecewise-uniform grids, optimal with respect to the order of convergence, for singularly perturbed convection-diffusion equations
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2002
%P 60-72
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2002_3_a7/
%G ru
%F IVM_2002_3_a7
G. I. Shishkin. Piecewise-uniform grids, optimal with respect to the order of convergence, for singularly perturbed convection-diffusion equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2002), pp. 60-72. http://geodesic.mathdoc.fr/item/IVM_2002_3_a7/

[1] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989, 608 pp. | MR

[2] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 616 pp. | MR

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

[4] Ilin A. M., “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Matem. zametki, 6:2 (1969), 237–248

[5] Dulan E., Miller Dzh., Shilders U., Ravnomernye chislennye metody resheniya zadach s pogranichnym sloem, Mir, M., 1983, 199 pp. | MR

[6] Shishkin G. I., Setochnye approksimatsii singulyarno vozmuschennykh ellipticheskikh i parabolicheskikh uravnenii, RAN, UrO, Ekaterinburg, 1992, 233 pp.

[7] Miller J. J. H., O'Riordan E., Shishkin G. I., Fitted numerical methods for singular perturbation problems, World Scientific, Singapore, 1996, 166 pp. | MR

[8] Roos H.-G., Stynes M., Tobiska L., Numerical methods for singularly perturbed differential equations. Convection-diffusion and flow problems, Springer-Verlag, Berlin, 1996, 348 pp. | MR

[9] Bagaev B. M., Shaidurov V. V., Setochnye metody resheniya zadach s pogranichnym sloem, Ch. 1, Nauka, Novosibirsk, 1998, 199 pp. | MR | Zbl

[10] Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E., Shishkin G. I., Robust computational techniques for boundary layers, CRC Press, Boca Raton, Florida, 2000, 254 pp. | MR | Zbl

[11] Vulanović R., Mesh construction for discretization of singularly perturbed boundary value problems, Ph. D. thesis, University of Novi Sad, 1986 | MR

[12] Shishkin G. I., “Raznostnaya skhema dlya singulyarno vozmuschennogo parabolicheskogo uravneniya s razryvnym granichnym usloviem”, Zhurn. vychisl. matem. i matem. fiz., 28:11 (1988), 1679–1692 | MR

[13] Linß T., “Analysis of a Galerkin finite element method on a Bakhvalov–Shishkin mesh for a linear convection-diffusion problem”, IMA J. Numer. Anal., 20:4 (2000), 621–632 | DOI | MR | Zbl

[14] Roos H.-G., Linß T., “Sufficient conditions for uniform convergence on layer-adapted grids”, Computing, 63:1 (1999), 27–45 | DOI | MR | Zbl

[15] Linß T., Roos H.-G., Vulanović R., “Uniform pointwise convergence on Shishkin-type meshes for quasilinear convection-diffusion problems”, SIAM J. Numer. Anal., 38:3 (2000), 897–912 | DOI | MR | Zbl

[16] Roos H.-G., “Layer-adapter grids for singular perturbation problems”, Z. Angew. Math. Mech., 78:5 (1998), 291–309 | 3.0.CO;2-R class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[17] Shishkin G. I., “Optimal piecewise uniform grids for singularly perturbed equations of a convection-diffusion type”, Rus. J. Numer. Anal. Math. Modelling, 16:2 (2001), 157–174 | MR | Zbl

[18] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR