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Volume 29, Issue 5
Finite Element Analysis of Optimal Control Problem Governed by Stokes Equations with $L^2$-Norm State-Constraints

Haifeng Niu & Danping Yang

J. Comp. Math., 29 (2011), pp. 589-604.

Published online: 2011-10

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  • Abstract

An optimal control problem governed by the Stokes equations with $L^2$-norm state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problems are discussed, and the a priori error estimates of the optimal order accuracy in $L^2$-norm and $H^1$-norm are given. Some numerical experiments are presented to verify the theoretical results.

  • AMS Subject Headings

49J20, 65N30.

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COPYRIGHT: © Global Science Press

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@Article{JCM-29-589, author = {}, title = {Finite Element Analysis of Optimal Control Problem Governed by Stokes Equations with $L^2$-Norm State-Constraints}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {5}, pages = {589--604}, abstract = {

An optimal control problem governed by the Stokes equations with $L^2$-norm state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problems are discussed, and the a priori error estimates of the optimal order accuracy in $L^2$-norm and $H^1$-norm are given. Some numerical experiments are presented to verify the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1103-m3514}, url = {http://global-sci.org/intro/article_detail/jcm/8494.html} }
TY - JOUR T1 - Finite Element Analysis of Optimal Control Problem Governed by Stokes Equations with $L^2$-Norm State-Constraints JO - Journal of Computational Mathematics VL - 5 SP - 589 EP - 604 PY - 2011 DA - 2011/10 SN - 29 DO - http://doi.org/10.4208/jcm.1103-m3514 UR - https://global-sci.org/intro/article_detail/jcm/8494.html KW - Optimal control, State constraints, Stokes equations, a priori error analysis. AB -

An optimal control problem governed by the Stokes equations with $L^2$-norm state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problems are discussed, and the a priori error estimates of the optimal order accuracy in $L^2$-norm and $H^1$-norm are given. Some numerical experiments are presented to verify the theoretical results.

Haifeng Niu & Danping Yang. (1970). Finite Element Analysis of Optimal Control Problem Governed by Stokes Equations with $L^2$-Norm State-Constraints. Journal of Computational Mathematics. 29 (5). 589-604. doi:10.4208/jcm.1103-m3514
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