Geodesic
On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 347-362 
Yu. M. Laevsky; O. V. Rudenko. On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 347-362. http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a5/
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     title = {On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with studying some modifications of the local one-dimensional schemes for solving the mixed and the third boundary value parabolic problems in nonrectangular domains. Contrary to the usual schemes with the error estimate $O(h+\tau/\sqrt h)$, these modifications have unconditional convergence with the error estimate $O(h+\tau)$ for the problem with the mixed boundary conditions of special type and $O(h+\tau^{5/6})$ for the third boundary value problem.

[1] Samarskii A. A., “Lokalno-odnomernye skhemy na neravnomernykh setkakh dlya uravnenii parabolicheskogo tipa”, Zhurn. vychisl. matem. i mat. fiziki, 3:3 (1963), 431–466 | MR | Zbl

[2] Lebedev V. I., Dyakonov E. G., “O primenenii raznostnykh skhem s rasscheplyayuschimsya operatorom dlya resheniya tretei kraevoi zadachi v sluchae uravnenii parabolicheskogo tipa”, Sib. mat. zhurn., 6:1 (1965), 108–113 | Zbl

[3] Fryazinov I. V., “O reshenii tretei kraevoi zadachi dlya dvumernogo uravneniya teploprovodnosti v proizvolnoi oblasti lokalno-odnomernym metodom”, Zhurn. vychisl. matem. i mat. fiziki, 6:3 (1966), 487–502

[4] Fryazinov I. V., “Ekonomichnye skhemy dlya uravneniya teploprovodnosti s kraevym usloviem III roda”, Zhurn. vychisl. matem i mat. fiziki, 12:3 (1972), 612–626

[5] Yanenko N. N., Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Nauka, Novosibirsk, 1967

[6] Laevsky Yu. M., Rudenko O. V., “Splitting methods for parabolic problems in nonrectangular domains”, Appl. Math. Lett., 8:6 (1995), 9–14 | DOI | MR | Zbl

[7] Laevskii Yu. M., Rudenko O. V., “O skhodimosti lokalno-odnomernykh skhem resheniya tretei kraevoi parabolicheskoi zadachi v nepryamougolnykh oblastyakh”, Dokl. RAN, 354:4 (1997), 452–455 | MR

[8] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[9] Laevskii Yu. M., Metod konechnykh elementov resheniya mnogomernykh parabolicheskikh uravnenii, Izd-vo NGU, Novosibirsk, 1993 | MR

[10] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo AN Arm. SSR, Erevan, 1979 | MR

[11] Konovalov A. N., Vvedenie v vychislitelnye metody lineinoi algebry, Nauka, Novosibirsk, 1993 | MR | Zbl