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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 4, Pages 381–396 (Mi sjvm450)  
This article is cited in 6 scientific papers (total in 6 papers)

Iterative proximal regularization of a modified Lagrangian functional for solving a semicoercive model problem with friction

N. N. Kushniruka, R. V. Nammb

a Amur State University, Blagoveshchensk
b Pacific National University, Khabarovsk
Full-text PDF (345 kB) Citations (6)
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Abstract: A problem of unconstrained minimization of a semicoercive nondifferentiable functional corresponding to a model friction problem is reduced to a problem of constrained minimization of a differentiable functional. An algorithm based on an iterative proximal regularization of a modified Lagrangian functional is used for solving the problem thus obtained. Convergence of a finite element solution is investigated. The results of numerical calculation are presented.
Key words: semicoercive friction problem, modified Lagrangian functional, saddle point, Udzava method, iterative proximal regularization, finite element method.
Received: 12.11.2010
Revised: 12.01.2011
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 4, Pages 319–332
DOI: https://doi.org/10.1134/S1995423911040057
Bibliographic databases:
Document Type: Article
UDC: 519.853.2+519.632
Language: Russian
Citation: N. N. Kushniruk, R. V. Namm, “Iterative proximal regularization of a modified Lagrangian functional for solving a semicoercive model problem with friction”, Sib. Zh. Vychisl. Mat., 14:4 (2011), 381–396; Num. Anal. Appl., 4:4 (2011), 319–332
Citation in format AMSBIB
\Bibitem{KusNam11}
\by N.~N.~Kushniruk, R.~V.~Namm
\paper Iterative proximal regularization of a~modified Lagrangian functional for solving a~semicoercive model problem with friction
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 4
\pages 381--396
\mathnet{http://mi.mathnet.ru/sjvm450}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 4
\pages 319--332
\crossref{https://doi.org/10.1134/S1995423911040057}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84155195827}
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  • https://www.mathnet.ru/eng/sjvm450
  • https://www.mathnet.ru/eng/sjvm/v14/i4/p381
    • This publication is cited in the following 6 articles:
    1. N. P. Lazarev, G. M. Semenova, “Equilibrium problem for a Timoshenko plate with a geometrically nonlinear condition of nonpenetration for a vertical crack”, J. Appl. Industr. Math., 14:3 (2020), 532–540  mathnet  crossref  crossref  elib
    2. N. P. Lazarev, I. Khiromiti, P. V. Sivtsev, I. M. Tikhonova, “O regulyarnosti resheniya v zadache o ravnovesii plastiny Timoshenko, soderzhaschei naklonnuyu treschinu”, Matematicheskie zametki SVFU, 25:1 (2018), 38–49  mathnet  crossref  elib
    3. N. P. Lazarev, “Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle”, J. Math. Sci., 203:4 (2014), 527–539  mathnet  crossref
    4. Lazarev N.P., “Zadacha o ravnovesii plastiny timoshenko, soderzhaschei treschinu na granitse uprugogo vklyucheniya s beskonechnoi zhestkostyu poperechnogo sdviga”, Prikladnaya mekhanika i tekhnicheskaya fizika, 2013, no. 2, 179–189  mathscinet  zmath  elib
    5. N. P. Lazarev, “Invariantnye integraly v zadache o ravnovesii plastiny Timoshenko s usloviyami tipa Sinorini na treschine”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 6(107), 100–115  mathnet
    6. N. P. Lazarev, “Extreme Crack Shapes in a Plate Timoshenko Model”, J. Math. Sci., 195:6 (2013), 815–826  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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