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Volume 13, Issue 2
Finite Element Method and Its Error Estimates for the Time Optimal Controls of Heat Equation

W. Gong & N.-N. Yan

Int. J. Numer. Anal. Mod., 13 (2016), pp. 265-279.

Published online: 2016-03

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  • Abstract

In this paper, we discuss the time optimal control problems governed by heat equation. The variational discretization concept is introduced for the approximation of the control, and the semi-discrete finite element method is applied for the controlled heat equation. We prove optimal a priori error estimate for the optimal time $T$, and quasi-optimal estimates for the optimal control $u$, the related state $y$ and adjoint state $p$.

  • Keywords

Time optimal control problems, finite element method, error estimates.

  • AMS Subject Headings

49J20, 49K20, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-265, author = {W. Gong and N.-N. Yan}, title = {Finite Element Method and Its Error Estimates for the Time Optimal Controls of Heat Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {2}, pages = {265--279}, abstract = {

In this paper, we discuss the time optimal control problems governed by heat equation. The variational discretization concept is introduced for the approximation of the control, and the semi-discrete finite element method is applied for the controlled heat equation. We prove optimal a priori error estimate for the optimal time $T$, and quasi-optimal estimates for the optimal control $u$, the related state $y$ and adjoint state $p$.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/438.html} }
TY - JOUR T1 - Finite Element Method and Its Error Estimates for the Time Optimal Controls of Heat Equation AU - W. Gong & N.-N. Yan JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 265 EP - 279 PY - 2016 DA - 2016/03 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/438.html KW - Time optimal control problems, finite element method, error estimates. AB -

In this paper, we discuss the time optimal control problems governed by heat equation. The variational discretization concept is introduced for the approximation of the control, and the semi-discrete finite element method is applied for the controlled heat equation. We prove optimal a priori error estimate for the optimal time $T$, and quasi-optimal estimates for the optimal control $u$, the related state $y$ and adjoint state $p$.

W. Gong and N.-N. Yan. (2016). Finite Element Method and Its Error Estimates for the Time Optimal Controls of Heat Equation. International Journal of Numerical Analysis and Modeling. 13 (2). 265-279. doi:
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