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Volume 4, Issue 4
Finite Element Approximation of Semilinear Parabolic Optimal Control Problems

Hongfei Fu & Hongxing Rui

DOI: 10.4208/nmtma.2011.m1020

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 489-504.

Published online: 2011-04

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  • Abstract

In this paper, the finite element approximation of a class of semilinear parabolic optimal control problems with pointwise control constraint is studied. We discretize the state and co-state variables by piecewise linear continuous functions, and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous functions. Some $\textit{a priori}$ error estimates are derived for both the control and state approximations. The convergence orders are also obtained.

  • Keywords

Finite element approximation, semilinear parabolic optimal control, pointwise control constraint, a priori error estimates.

  • AMS Subject Headings

49J20, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-489, author = {Hongfei Fu and Hongxing Rui}, title = {Finite Element Approximation of Semilinear Parabolic Optimal Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {4}, pages = {489--504}, abstract = {

In this paper, the finite element approximation of a class of semilinear parabolic optimal control problems with pointwise control constraint is studied. We discretize the state and co-state variables by piecewise linear continuous functions, and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous functions. Some $\textit{a priori}$ error estimates are derived for both the control and state approximations. The convergence orders are also obtained.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1020}, url = {http://global-sci.org/intro/article_detail/nmtma/5980.html} }
TY - JOUR T1 - Finite Element Approximation of Semilinear Parabolic Optimal Control Problems AU - Hongfei Fu & Hongxing Rui JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 489 EP - 504 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1020 UR - https://global-sci.org/intro/article_detail/nmtma/5980.html KW - Finite element approximation, semilinear parabolic optimal control, pointwise control constraint, a priori error estimates. AB -

In this paper, the finite element approximation of a class of semilinear parabolic optimal control problems with pointwise control constraint is studied. We discretize the state and co-state variables by piecewise linear continuous functions, and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous functions. Some $\textit{a priori}$ error estimates are derived for both the control and state approximations. The convergence orders are also obtained.

Hongfei Fu and Hongxing Rui. (2011). Finite Element Approximation of Semilinear Parabolic Optimal Control Problems. Numerical Mathematics: Theory, Methods and Applications. 4 (4). 489-504. doi:10.4208/nmtma.2011.m1020
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