Geodesic
Solution of a~semicoercive Signorini problem by a~method of iterative proximal regularization of a~modified Lagrange functional
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 36-45.

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

Duality methods based on classical schemes for constructing Lagrange functionals are inapplicable for solving semicoercive variational inequalities in mechanics. In this paper we approximately solve a scalar semicoercive Signorini problem, using a duality method based on the iterative proximal regularization of a modified Lagrange functional. We realize the algorithm with the help of the finite element method on a sequence of domain triangulations.
Keywords: functional, saddle point, iterative regularization, Uzawa method, finite elements.
Mots-clés : triangulation 
@article{IVM_2010_4_a3,
     author = {R. V. Namm and A. S. Tkachenko},
     title = {Solution of a~semicoercive {Signorini} problem by a~method of iterative proximal regularization of a~modified {Lagrange} functional},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--45},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_4_a3/}
}
TY  - JOUR
AU  - R. V. Namm
AU  - A. S. Tkachenko
TI  - Solution of a~semicoercive Signorini problem by a~method of iterative proximal regularization of a~modified Lagrange functional
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 36
EP  - 45
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_4_a3/
LA  - ru
ID  - IVM_2010_4_a3
ER  - 
%0 Journal Article
%A R. V. Namm
%A A. S. Tkachenko
%T Solution of a~semicoercive Signorini problem by a~method of iterative proximal regularization of a~modified Lagrange functional
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 36-45
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_4_a3/
%G ru
%F IVM_2010_4_a3
R. V. Namm; A. S. Tkachenko. Solution of a~semicoercive Signorini problem by a~method of iterative proximal regularization of a~modified Lagrange functional. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 36-45. http://geodesic.mathdoc.fr/item/IVM_2010_4_a3/

[1] 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 matem. fiz., 46:1 (2006), 26–36 | MR | Zbl

[2] Vu G., Kim S., Namm R. V., Sachkov S. A., “Metod iterativnoi proksimalnoi regulyarizatsii dlya poiska sedlovoi tochki v polukoertsitivnoi zadache Sinorini”, Zhurn. vychisl. matem. i matem. fiz., 46:11 (2006), 2024–2031 | MR

[3] Glavachek I., Gaslinger Ya., Nechas I., Lovishek Ya., Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986, 270 pp. | MR

[4] Dyuvo G., Lions Zh.-L., Neravenstva v fizike i mekhanike, Nauka, M., 1980, 382 pp.

[5] Glovinski R., Lions Zh.-L., Tremoler R., Chislennoe issledovanie variatsionnykh neravenstv, Mir, M., 1979, 576 pp. | MR

[6] Glowinski R., Numerical methods for nonlinear variational problems, Springer, N.Y., 1984, 493 pp. | MR | Zbl

[7] Brezis H., “Problèmes unilatéraux”, J. Math. Pur. Appl., 51 (1972), 1–168 | MR | Zbl

[8] Grisvard P., Boundary value problems in nonsmooth domains, Univ. Dept. Math., College Park, MD, Maryland, 1980

[9] Ekland I., Temam R., Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979, 400 pp. | MR

[10] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981, 400 pp. | MR

[11] 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