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Volume 26, Issue 4
A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type

Danping Yang, Yanzhen Chang & Wenbin Liu

J. Comp. Math., 26 (2008), pp. 471-487.

Published online: 2008-08

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  • Abstract

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal $L^2$-norm error estimates and the almost optimal $L^\infty$-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.

  • Keywords

Bilinear control problem, Finite element approximation, Superconvergence, A priori error estimate, A posteriori error estimator.

  • AMS Subject Headings

49J20, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-26-471, author = {Danping Yang, Yanzhen Chang and Wenbin Liu}, title = {A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {4}, pages = {471--487}, abstract = {

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal $L^2$-norm error estimates and the almost optimal $L^\infty$-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8638.html} }
TY - JOUR T1 - A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type AU - Danping Yang, Yanzhen Chang & Wenbin Liu JO - Journal of Computational Mathematics VL - 4 SP - 471 EP - 487 PY - 2008 DA - 2008/08 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8638.html KW - Bilinear control problem, Finite element approximation, Superconvergence, A priori error estimate, A posteriori error estimator. AB -

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal $L^2$-norm error estimates and the almost optimal $L^\infty$-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.

Danping Yang, Yanzhen Chang and Wenbin Liu. (2008). A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type. Journal of Computational Mathematics. 26 (4). 471-487. doi:
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