On a~stable duality scheme method for solution of the Mosolov and the Miasnikov problem with boundary friction
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 4, pp. 351-365.

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

The paper deals with the construction of a stable method for solution of the Mosolov and the Miasnikov variational problem with boundary friction and can be considered as the sequel of the investigations started in [1]. An approximate solution is carried out on the basis of the iterative prox-regularization method. In this case, each auxiliary problem is coming to the search of the Lagrange functional saddle point. The error estimation is defined for the numerical solution of the problem in the case of realization of this algorithm using the finite element method on a sequence of triangulations. The results of numerical computations are presented.
@article{SJVM_2002_5_4_a3,
     author = {R. V. Namm and S. A. Sachkov},
     title = {On a~stable duality scheme method for solution of the {Mosolov} and the {Miasnikov} problem with boundary friction},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {351--365},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a3/}
}
TY  - JOUR
AU  - R. V. Namm
AU  - S. A. Sachkov
TI  - On a~stable duality scheme method for solution of the Mosolov and the Miasnikov problem with boundary friction
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2002
SP  - 351
EP  - 365
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a3/
LA  - ru
ID  - SJVM_2002_5_4_a3
ER  - 
%0 Journal Article
%A R. V. Namm
%A S. A. Sachkov
%T On a~stable duality scheme method for solution of the Mosolov and the Miasnikov problem with boundary friction
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2002
%P 351-365
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a3/
%G ru
%F SJVM_2002_5_4_a3
R. V. Namm; S. A. Sachkov. On a~stable duality scheme method for solution of the Mosolov and the Miasnikov problem with boundary friction. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 4, pp. 351-365. http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a3/

[1] Zolotukhin A. Ya., Namm R. V., Pachina A. V., “Priblizhennoe reshenie variatsionnoi zadachi Mosolova i Myasnikova s treniem na granitse po zakonu Kulona”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 4:2 (2001), 163–177 | MR | Zbl

[2] Mosolov P. P., Myasnikov V. P., Mekhanika zhestkoplasticheskikh sred, Nauka. Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1981 | MR | Zbl

[3] Fortin A., Cote D., “On the imposition of friction boundary conditions for numerical simulation of Bingham fluid flows”, Computer Methods in Applied Mechanics and Engineering 88, North-Holland, 1991, 97–109

[4] Kaplan A. A., Namm R. V., “Ob otsenke skorosti skhodimosti iteratsionnykh protsessov s prox-regulyarizatsiei”, Issledovaniya po uslovnoi korrektnosti zadach matematicheskoi fiziki, Novosibirsk, 1989, 60–77 | MR

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

[6] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[7] Sachkov S. A., Metod resheniya zadachi Mosolova i Myasnikova s treniem na granitse, osnovannyi na printsipakh dvoistvennosti, Preprint DVO RAN. Vychislitelnyi tsentr; 2001/56, Khabarovsk, 2001

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

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