On some finite-difference approximations of Stokes problem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 573-580.

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

Several finite-difference schemes for the Stokes problem satisfying the Ladyzhenskaya–Babuska–Brezzi condition are considered. These schemes use staggered meshes (MAC–schemes) in rectangular domains. The aim of investigations is to obtain a dependence of a constant in the LBB–condition on geometric and grid parameters for a scheme and a comparative analysis of schemes with respect to the data obtained. Discrete eigenvalue problems were solved with high precision. Results of some three-dimensional calculations are presented.
@article{FPM_1995_1_3_a0,
     author = {P. P. Aristov and E. V. Chizhonkov},
     title = {On some finite-difference approximations of {Stokes} problem},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {573--580},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a0/}
}
TY  - JOUR
AU  - P. P. Aristov
AU  - E. V. Chizhonkov
TI  - On some finite-difference approximations of Stokes problem
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1995
SP  - 573
EP  - 580
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a0/
LA  - ru
ID  - FPM_1995_1_3_a0
ER  - 
%0 Journal Article
%A P. P. Aristov
%A E. V. Chizhonkov
%T On some finite-difference approximations of Stokes problem
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1995
%P 573-580
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a0/
%G ru
%F FPM_1995_1_3_a0
P. P. Aristov; E. V. Chizhonkov. On some finite-difference approximations of Stokes problem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 573-580. http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a0/

[1] Gunzburger M. D., Finite Elemet Methods for Viscous Incompressible Flows. A Guide to Theory, Practice, and Algorithms, Academic Press, Inc., 1989 | MR | Zbl

[2] Kobelkov G. M., “O chislennykh metodakh resheniya uravnenii Nave–Stoksa v peremennykh skorost–davlenie”, Vychislitelnye protsessy i sistemy, 8, Nauka, M., 1991, 204–236 | MR

[3] Dyakonov E. G., Minimizatsiya vychislitelnoi raboty. Asimptoticheski optimalnye algoritmy dlya ellipticheskikh zadach, Nauka, M., 1989 | MR

[4] Aristov P. P., “Ob uskorenii skhodimosti odnogo iteratsionnogo metoda resheniya zadachi Stoksa”, Izvestiya vuzov. Matematika, 1994, no. 9, 3–10 | MR | Zbl

[5] Chizhonkov E. V., “O skhodimosti odnogo algoritma dlya resheniya zadachi Stoksa”, Vestnik Mosk. Un-ta. Ser. 15, vychisl. matem. i kibern., 1995, no. 2, 12–17 | MR | Zbl

[6] Nicolaides R. A., “Analysis and convergence of the MAC scheme. The linear problem”, SIAM Journ. Numer. Anal., 29:6 (1992), 1579–1591 | DOI | MR | Zbl

[7] Daly B. J., Harlow F. H., Shannon J. P., Welch J. E., The MAC Method, Technical Report LA-3425., Los Alamos Scientific Lab., University of California, 1965

[8] Lebedev V. I., “Raznostnye analogi ortogonalnykh razlozhenii, fundamentalnykh differentsialnykh operatorov i osnovnykh nachalno-kraevykh zadach matematicheskoi fiziki”, ZhVM i MF, 4:6 (1964), 449–465 | MR | Zbl

[9] Bakhvalov N. S., Kobelkov G. M., Chizhonkov E. V., “Effektivnye metody resheniya uravnenii Nave–Stoksa”, Chislennoe modelirovanie v aerogidrodinamike, Nauka, M., 1986, 37–45

[10] Isakov A. B., Kobelkov G. M., K chislennomu resheniyu zadachi o dvizhenii vyazkoi neszhimaemoi zhidkosti v kubicheskoi kaverne, Preprint OVM AN SSSR, no. 179, M., 1987

[11] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR

[12] Parlett B., Simmetrichnaya problema sobstvennykh znachenii, Mir, M., 1983 | MR | Zbl

[13] Zarubezhnye biblioteki i pakety programm po vychislitelnoi matematike, ed. U. Kauella, Nauka, M., 1993 | MR

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