Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

Ruo Li; Wenbin Liu; Heping Ma; Tao Tang

doi:10.1137/S0363012901389342

Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

Ruo Li, Wenbin Liu, Heping Ma, Tao Tang

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

245 Citations (Scopus)

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Abstract

In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work.

Original language	English
Pages (from-to)	1321-1349
Number of pages	29
Journal	SIAM Journal on Control and Optimization
Volume	41
Issue number	5
DOIs	https://doi.org/10.1137/S0363012901389342
Publication status	Published - Sept 2002

Scopus Subject Areas

Control and Optimization
Applied Mathematics

User-Defined Keywords

A posteriori error estimate
Finite element method
Mesh adaptivity
Optimal control

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10.1137/S0363012901389342

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abstract = "In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work.",

keywords = "A posteriori error estimate, Finite element method, Mesh adaptivity, Optimal control",

author = "Ruo Li and Wenbin Liu and Heping Ma and Tao Tang",

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AU - Li, Ruo

AU - Liu, Wenbin

AU - Ma, Heping

AU - Tang, Tao

N1 - Funding information: This work was supported in part by Hong Kong Baptist University, Hong Kong Research Grants Council, and the British EPSRC. Publisher copyright: Copyright © 2002 Society for Industrial and Applied Mathematics

PY - 2002/9

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N2 - In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work.

AB - In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work.

KW - A posteriori error estimate

KW - Finite element method

KW - Mesh adaptivity

KW - Optimal control

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Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

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