Geodesic
A modified dual scheme for solving an elastic crack problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 47-58 
R. V. Namm; G. I. Tsoy. A modified dual scheme for solving an elastic crack problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 47-58. http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a4/
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     title = {A modified dual scheme for solving an elastic crack problem},
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     pages = {47--58},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The dual scheme for solving a crack problem in terms of displacements is considered. The dual solution method is based on a modified Lagrangian functional. In addition, the method convergence is investigated under natural assumptions on $H^1$-regularity of the crack problem solution. The duality relation for the primal and dual problems has been proposed.

[1] Morozov N. F., Matematicheskie voprosy teorii treschin, Nauka, M., 1984

[2] Khludnev A. M., Zadachi teorii uprugosti v negladkikh oblastyakh, Fizmatlit, M., 2010

[3] Kravchuk A. S., Variatsionnye i kvazivariatsionnye neravenstva v mekhanike, MGAPI, M., 1997

[4] Khludnev A. M., Kovtunenko V. A., Analysis of crack in solids, WIT Press, Southhampton–Boston, 2000

[5] Vu G., Namm R. V., Sachkov S. A., “Iteratsionnyi metod poiska sedlovoi tochki dlya polukoertsitivnoi zadachi Sinorini, osnovannyi na modifitsirovannom funktsionale Lagranzha”, Zhurn. vychisl. matem. i mat. fiziki, 46:1 (2006), 26–36 | MR | Zbl

[6] Vikhtenko E. M., Namm R. V., “Skhema dvoistvennosti dlya resheniya polukoertsitivnoi zadachi Sinorini s treniem”, Zhurn. vychisl. matem. i mat. fiziki, 47:12 (2007), 2023–2036 | MR

[7] Vikhtenko E. M., Maksimova N. N., Namm R. V., “Funktsionaly chuvstvitelnosti v variatsionnykh neravenstvakh mekhaniki i ikh prilozhenie k skhemam dvoistvennosti”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 17:1 (2014), 43–52 | MR | Zbl

[8] Vikhtenko E. M., Vu G., Namm R. V., “Funktsionaly chuvstvitelnosti v kontaktnykh zadachakh teorii uprugosti”, Zhurn. vychisl. matem. i mat. fiziki, 54:7 (2014), 1218–1228 | DOI | MR | Zbl

[9] Vikhtenko E. M., Namm R. V., “O metode dvoistvennosti dlya resheniya modelnoi zadachi s treschinoi”, Tr. IMM UrO RAN, 22, no. 1, 2016, 36–43 | MR

[10] Kufner A., Fuchik S., Nelineinye differentsialnye uravneniya, Nauka, M., 1988

[11] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981

[12] Vikhtenko E. M., Vu G., Namm R. V., “Metody resheniya polukoertsitivnykh variatsionnykh neravenstv mekhaniki na osnove modifitsirovannykh funktsionalov Lagranzha”, Dalnevostoch. mat. zhurn., 14:1 (2014), 6–17 | MR | Zbl

[13] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Fizmatlit, M., 1981

[14] Hintermuller M., Kovtunenko V. A., Kunisch K., “The primal-dual active set method for a crack problem with non-penetration”, IMA J. Appl. Math., 69:1 (2004), 1–26 | DOI | MR | Zbl

[15] Vtorushin E. V., “Chislennoe issledovanie modelnoi zadachi deformirovaniya uprugoplasticheskogo tela s treschinoi pri uslovii vozmozhnogo kontakta beregov”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 9:4 (2006), 335–344 | Zbl