Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 489-504.
Published online: 2011-04
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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} }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.