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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

DOI: 10.4208/jcm.1103-m3514

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.

  • Keywords

Optimal control, State constraints, Stokes equations, a priori error analysis.

  • AMS Subject Headings

49J20, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-589, author = {Haifeng Niu and Danping Yang}, 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 AU - Haifeng Niu & Danping Yang 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 and Danping Yang. (2011). 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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