On the convergence of the Uzawa method with a modified Lagrange functional for variational inequalities in mechanics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1357-1366 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the scalar semicoercive Signorini problem, the dual problem is constructed on the basis of a modified Lagrangian functional. The convergence of the gradient method as applied to solving the dual problem is examined.
@article{ZVMMF_2010_50_8_a1,
     author = {\`E. M. Vikhtenko and G. Vu and R. V. Namm},
     title = {On the convergence of the {Uzawa} method with a modified {Lagrange} functional for variational inequalities in mechanics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1357--1366},
     year = {2010},
     volume = {50},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a1/}
}
TY  - JOUR
AU  - È. M. Vikhtenko
AU  - G. Vu
AU  - R. V. Namm
TI  - On the convergence of the Uzawa method with a modified Lagrange functional for variational inequalities in mechanics
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1357
EP  - 1366
VL  - 50
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a1/
LA  - ru
ID  - ZVMMF_2010_50_8_a1
ER  - 
%0 Journal Article
%A È. M. Vikhtenko
%A G. Vu
%A R. V. Namm
%T On the convergence of the Uzawa method with a modified Lagrange functional for variational inequalities in mechanics
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1357-1366
%V 50
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a1/
%G ru
%F ZVMMF_2010_50_8_a1
È. M. Vikhtenko; G. Vu; R. V. Namm. On the convergence of the Uzawa method with a modified Lagrange functional for variational inequalities in mechanics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1357-1366. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a1/

[1] Glovinski R., Lions Zh.-L., Tremoler R., Chislennoe issledovanie variatsionnykh neravenstv, Mir, M., 1979 | MR

[2] Glowinski R., Numerical methods for nonlinear variational problems, Springer, New York, 1984 | MR | Zbl

[3] Glavachek I., Gaslinger Ya., Nechas I., Lovishek Ya., Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986 | MR

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

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

[6] Namm R. V., Sachkov S. A., “Reshenie kvazivariatsionnogo neravenstva Sinorini metodom posledovatelnykh priblizhenii”, Zh. vychisl. matem. i matem. fiz., 49:5 (2009), 805–814 | MR | Zbl

[7] Kushniruk N. N., Namm R. V., “Metod mnozhitelei Lagranzha dlya resheniya polukoertsitivnoi modelnoi zadachi s treniem”, Sibirskii zhurnal vychisl. matem., 12:4 (2009), 409–420 | Zbl

[8] Kikuchi N., Oden T., Contact problem in elasticity: a study of variational inequalities and finite element methods, SIAM, Philadelphia, 1988 | MR | Zbl

[9] Dyuvo G., Lions Zh.-L., Neravenstva v mekhanike i fizike, Nauka, M., 1980 | MR

[10] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[11] Grossman K., Kaplan A. A., Nelineinoe programmirovanie na osnove bezuslovnoi minimizatsii, Nauka, Novosibirsk, 1981 | Zbl

[12] Namm R. V., Podgaev A. G., “O $W_2^2$ regulyarnosti reshenii polukoertsitivnykh variatsionnykh neravenstv”, Dalnevostochnyi matem. zhurnal, 3:2 (2002), 210–215

[13] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[14] Gilbarg D., Trudinger M., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi, Nauka, M., 1989 | Zbl

[15] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. matem. ob-va, 1967, 227–313

[16] Grisvard P., Boundary value problems in non-smooth domains, Univ. Dept. Math. College Park, MD, Maryland, 1980

[17] Vikhtenko E. M., Namm R. V., “O metode resheniya polukoertsitivnykh variatsionnykh neravenstv, osnovannom na metode iterativnoi proksimalnoi regulyarizatsii”, Izv. vuzov. Matematika, 2004, no. 1, 31–35 | MR | Zbl