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Volume 10, Issue 1
Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations

Tongjun Sun, Liang Ge & Wenbin Liu

Int. J. Numer. Anal. Mod., 10 (2013), pp. 1-23.

Published online: 2013-10

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  • Abstract

In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic equations on multi-meshes. The control constraint is given in an integral sense: $K = \{u(t) ∈ L^2( Ω) : a ≤ ∫_ Ω u(t) ≤ b\}$. We derive equivalent a posteriori error estimates with lower and upper bounds for both the state and the control approximation, which are used as indicators in adaptive multi-meshes finite element scheme. The error estimates are then implemented and tested with promising numerical experiments.

  • Keywords

constrained optimal control problem, adaptive finite element approximation, equivalent a posteriori error estimates, parabolic equations, multi-meshes.

  • AMS Subject Headings

65N30, 49J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-1, author = {Sun , TongjunGe , Liang and Liu , Wenbin}, title = {Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {1}, pages = {1--23}, abstract = {

In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic equations on multi-meshes. The control constraint is given in an integral sense: $K = \{u(t) ∈ L^2( Ω) : a ≤ ∫_ Ω u(t) ≤ b\}$. We derive equivalent a posteriori error estimates with lower and upper bounds for both the state and the control approximation, which are used as indicators in adaptive multi-meshes finite element scheme. The error estimates are then implemented and tested with promising numerical experiments.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/556.html} }
TY - JOUR T1 - Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations AU - Sun , Tongjun AU - Ge , Liang AU - Liu , Wenbin JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 23 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/556.html KW - constrained optimal control problem, adaptive finite element approximation, equivalent a posteriori error estimates, parabolic equations, multi-meshes. AB -

In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic equations on multi-meshes. The control constraint is given in an integral sense: $K = \{u(t) ∈ L^2( Ω) : a ≤ ∫_ Ω u(t) ≤ b\}$. We derive equivalent a posteriori error estimates with lower and upper bounds for both the state and the control approximation, which are used as indicators in adaptive multi-meshes finite element scheme. The error estimates are then implemented and tested with promising numerical experiments.

Sun , TongjunGe , Liang and Liu , Wenbin. (2013). Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations. International Journal of Numerical Analysis and Modeling. 10 (1). 1-23. doi:
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