Geodesic
Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 7 (2007) no. 3, pp. 73-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper deals with numerical solution to first boundary-value problem for degenerate 2D elliptic equation using finite-element method. Degeneration of the operator on a part of the boundary requires using weighted functional spaces to analyze variational statement, build difference scheme and prove convergence. We prove that for finite-element method with piece-wise linear elements convergence rate is not worse than in the case of non-degenerating equation. In the last section we demonstrate numerical example to confirm convergence rate. 
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V. O. Pirogov; M. V. Urev. Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 7 (2007) no. 3, pp. 73-85. http://geodesic.mathdoc.fr/item/VNGU_2007_7_3_a4/

[1] Gusman Yu. A., Oganesyan L. A., “Otsenki skhodimosti konechno-raznostnykh skhem dlya vyrozhdennykh ellipticheskikh uravnenii”, Zhurn. vychisl. mat. i mat. fiziki, 5:2 (1965), 351–357 | MR

[2] Urev M. V., “Skhodimost metoda konechnykh elementov dlya osesimmetrichnoi zadachi magnitostatiki”, Sib. zhurn. vychisl. mat., 9:1 (2006), 63–79 | MR | Zbl

[3] Samarskii A. A., Lazarov R. D., Makarov V. L., Raznostnye skhemy dlya differentsialnykh uravnenii s obobschennymi resheniyami, Vysshaya shkola, M., 1987

[4] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo AN ArmSSR, Erevan, 1979

[5] Nikolskii S. M., Lizorkin P. I., Miroshin N. V., “Vesovye funktsionalnye prostranstva i ikh prilozheniya k issledovaniyu kraevykh zadach dlya vyrozhdayuschikhsya ellipticheskikh uravnenii”, Izv. vuzov. Matematika, 1988, no. 8, 4–30

[6] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

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

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

[9] Ilin V. P., Metody nepolnoi faktorizatsii dlya resheniya algebraicheskikh sistem, Fizmatlit, M., 1995 | MR