Zuliang Lu, Yanping Chen, “$L^\infty$-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations”, Sib. Zh. Vychisl. Mat., 12:1 (2009), 91–105; Num. Anal. Appl., 2:1 (2009), 74

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2009, Volume 12, Number 1, Pages 91–105 (Mi sjvm7)

This article is cited in 54 scientific papers (total in 54 papers)

L^{\infty}

$L^\infty$ -error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations

Zuliang Lu^a, Yanping Chen^b

^a Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, P.R. of China
^b School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. of China

Full-text PDF (440 kB) Citations (54)

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Abstract: In this paper, we investigate

L^{\infty}

$L^\infty$ -error estimates for convex quadratic optimal control problems governed by nonlinear elliptic partial differential equations using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive

L^{\infty}

$L^\infty$ -error estimates of optimal order for a mixed finite element approximation of a semilinear elliptic optimal control problem. Finally, we present numerical tests which confirm our theoretical results.

Key words:

L^{\infty}

$L^\infty$ -error estimates, optimal control problem, semilinear elliptic equation, mixed finite element methods.

Received: 02.06.2008
Revised: 17.07.2008

English version:
Numerical Analysis and Applications, 2009, Volume 2, Issue 1, Pages 74–86
DOI: https://doi.org/10.1134/S1995423909010078

Bibliographic databases:

UDC: 517.93+519.713:007.52

Language: Russian

Citation: Zuliang Lu, Yanping Chen, “

L^{\infty}

$L^\infty$ -error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations”, Sib. Zh. Vychisl. Mat., 12:1 (2009), 91–105; Num. Anal. Appl., 2:1 (2009), 74–86

Citation in format AMSBIB

\Bibitem{ZulChe09}

\by Zuliang Lu, Yanping Chen

\paper $L^\infty$-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations

\jour Sib. Zh. Vychisl. Mat.

\yr 2009

\vol 12

\issue 1

\pages 91--105

\mathnet{http://mi.mathnet.ru/sjvm7}

\transl

\jour Num. Anal. Appl.

\yr 2009

\vol 2

\issue 1

\pages 74--86

\crossref{https://doi.org/10.1134/S1995423909010078}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65249097240}

Linking options:

https://www.mathnet.ru/eng/sjvm7

https://www.mathnet.ru/eng/sjvm/v12/i1/p91

This publication is cited in the following 54 articles:

Changil Kim, Jayong Ri, “A Priori and a Posteriori Error Estimates of Finite Element Method for Source Control Problems Governed by a System of Quasi-linear Elliptic Equations”, IJTAM, 11:1 (2025), 1
Changling Xu, Hongbo Chen, “A two-grid $P_0^2$ - $P_1$ mixed finite element scheme for semilinear elliptic optimal control problems”, MATH, 7:4 (2022), 6153
Chunjuan Hou, Zuliang Lu, Xuejiao Chen, Xiankui Wu, Fei Cai, “Superconvergence for optimal control problems governed by semilinear parabolic equations”, MATH, 7:5 (2022), 9405
Lu Z., Cao L., Li L., “Interpolation Coefficients Mixed Finite Element Methods For General Semilinear Dirichlet Boundary Elliptic Optimal Control Problems”, Appl. Anal., 97:14 (2018), 2496–2509
Lu Z., Zhang Sh., “L-Infinity-Error Estimates of Rectangular Mixed Finite Element Methods For Bilinear Optimal Control Problem”, Appl. Math. Comput., 300 (2017), 79–94
Manickam K., Prakash P., “Mixed Finite Element Methods For Fourth Order Elliptic Optimal Control Problems”, Numer. Math.-Theory Methods Appl., 9:4 (2016), 528–548
Lu Z., “A Posteriori Error Estimates of Triangular Mixed Finite Element Methods For Quadratic Convection Diffusion Optimal Control Problems”, Math. Rep., 18:3 (2016), 335–354
Lu Z., “a Residual-Based Posteriori Error Estimates For Hp Finite Element Solutions of General Bilinear Optimal Control Problems”, J. Math. Inequal., 9:3 (2015), 665–682
Hou Ch., Chen Ya., Lu Z., “a Posteriori Error Estimates of Mixed Finite Element Solutions For Fourth Order Parabolic Control Problems”, J. Inequal. Appl., 2015, 240
Hou T., “Error Estimates of Rt1 Mixed Methods for Distributed Optimal Control Problems”, Bull. Korean. Math. Soc., 51:1 (2014), 139–156
Lu Z., “L-Infinity-Estimates of Rectangular Mixed Methods for Nonlinear Constrained Optimal Control Problem”, Bull. Malays. Math. Sci. Soc., 37:1 (2014), 271–284
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
Lu Z., Huang X., “a Priori Error Estimates of Mixed Finite Element Methods For General Linear Hyperbolic Convex Optimal Control Problems”, Abstract Appl. Anal., 2014, 547490
Z. Lu, D. Liu, “A posteriori error estimates for boundary parabolic optimal control problems”, Lobachevskii J Math, 35:2 (2014), 92
T. Hou, “Superconvergence and a posteriori error estimates of RT1 mixed methods for elliptic control problems with an integral constraint”, Num. Anal. Appl., 6:2 (2013), 163–175
Chen Ya., Hou T., “Error Estimates and Superconvergence of Rt0 Mixed Methods for a Class of Semilinear Elliptic Optimal Control Problems!”, Numer. Math.-Theory Methods Appl., 6:4 (2013), 637–656
Chen Ya., Lu Z., Huang Yu., “Superconvergence of Triangular Raviart-Thomas Mixed Finite Element Methods for a Bilinear Constrained Optimal Control Problem”, Comput. Math. Appl., 66:8 (2013), 1498–1513
Hou T., “Superconvergence and l-Infinity-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations”, Numer. Math.-Theory Methods Appl., 6:3 (2013), 479–498
Lu Z., Liu D., “A Posteriori Error Estimates of Variational Discretization Mixed Finite Element Methods for Integro-Differential Optimal Control Problem”, 2013 10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), IEEE, 2013, 37–41
Lu Z., “Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint”, J. Appl. Math., 2013, 302935

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