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Volume 27, Issue 4
A Posteriori Error Estimate of Optimal Control Problem of PDE with Integral Constraint for State

Lei Yuan & Danping Yang

DOI: 10.4208/jcm.2009.27.4.017

J. Comp. Math., 27 (2009), pp. 525-542.

Published online: 2009-08

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  • Abstract

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.

  • Keywords

State-constrained optimal control problem, Adaptive finite element method, A posteriori error estimate.

  • AMS Subject Headings

49J20, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-525, author = {Lei Yuan and Danping Yang}, title = {A Posteriori Error Estimate of Optimal Control Problem of PDE with Integral Constraint for State}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {4}, pages = {525--542}, abstract = {

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.4.017}, url = {http://global-sci.org/intro/article_detail/jcm/8587.html} }
TY - JOUR T1 - A Posteriori Error Estimate of Optimal Control Problem of PDE with Integral Constraint for State AU - Lei Yuan & Danping Yang JO - Journal of Computational Mathematics VL - 4 SP - 525 EP - 542 PY - 2009 DA - 2009/08 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.4.017 UR - https://global-sci.org/intro/article_detail/jcm/8587.html KW - State-constrained optimal control problem, Adaptive finite element method, A posteriori error estimate. AB -

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.

Lei Yuan and Danping Yang. (2009). A Posteriori Error Estimate of Optimal Control Problem of PDE with Integral Constraint for State. Journal of Computational Mathematics. 27 (4). 525-542. doi:10.4208/jcm.2009.27.4.017
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