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

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

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• RIS
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@Article{NMTMA-4-489, author = {}, 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 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 & Hongxing Rui. (2020). 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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