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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 3, Pages 261–276 (Mi sjvm440)  
This article is cited in 5 scientific papers (total in 5 papers)

A posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem

Z. Luab

a College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, China
b College of Mathematics and Computer Sciences, Chongqing Three Gorges University, Chongqing, China
Full-text PDF (303 kB) Citations (5)
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Abstract: This paper is aimed at studying finite element discretization for a class of quadratic boundary optimal control problems governed by nonlinear elliptic equations. We derive a posteriori error estimates for the coupled state and control approximation. Such estimates can be used to construct a reliable adaptive finite element approximation for the boundary optimal control problem. Finally, we present a numerical example to confirm our theoretical results.
Key words: nonlinear boundary optimal control problem, finite element methods, a posteriori error estimates.
Received: 14.11.2010
Revised: 22.12.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 3, Pages 210–222
DOI: https://doi.org/10.1134/S1995423911030037
Bibliographic databases:
Document Type: Article
UDC: 517.93+519.713+007.52
Language: Russian
Citation: Z. Lu, “A posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem”, Sib. Zh. Vychisl. Mat., 14:3 (2011), 261–276; Num. Anal. Appl., 4:3 (2011), 210–222
Citation in format AMSBIB
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\by Z.~Lu
\paper A~posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 3
\pages 261--276
\mathnet{http://mi.mathnet.ru/sjvm440}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 3
\pages 210--222
\crossref{https://doi.org/10.1134/S1995423911030037}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79960829855}
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  • https://www.mathnet.ru/eng/sjvm440
  • https://www.mathnet.ru/eng/sjvm/v14/i3/p261
    • This publication is cited in the following 5 articles:
    1. Lu Z., “a Posteriori Error Estimates of Fully Discrete Finite-Element Schemes For Nonlinear Parabolic Integro-Differential Optimal Control Problems”, Adv. Differ. Equ., 2014, 15  crossref  mathscinet  isi  scopus
    2. Z. Lu, D. Liu, “A posteriori error estimates for boundary parabolic optimal control problems”, Lobachevskii J Math, 35:2 (2014), 92  crossref
    3. Lu Z., “Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint”, J. Appl. Math., 2013, 302935  crossref  mathscinet  isi  scopus
    4. Lu Z., “Adaptive Fully-Discrete Finite Element Methods for Nonlinear Quadratic Parabolic Boundary Optimal Control”, Bound. Value Probl., 2013, 72, 1–18  crossref  mathscinet  isi  scopus
    5. Yan Ningning, 2007 Chinese Control Conference, 2006, 621  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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