Abstract
This paper studies variational discretization for the optimal control problem governed by parabolic equations with control constraints. First of all, the authors derive a priori error estimates where \(\left\| {\left| {u - U_h } \right|} \right\|_{L^\infty \left( {J;L^2 \left( \Omega \right)} \right)} = O\left( {h^2 + k} \right)\). It is much better than a priori error estimates of standard finite element and backward Euler method where \(\left\| {\left| {u - U_h } \right|} \right\|_{L^\infty \left( {J;L^2 \left( \Omega \right)} \right)} = O\left( {h + k} \right)\). Secondly, the authors obtain a posteriori error estimates of residual type. Finally, the authors present some numerical algorithms for the optimal control problem and do some numerical experiments to illustrate their theoretical results.
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This research is supported by National Science Foundation of China, Foundation for Talent Introduction of Guangdong Provincial University, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), Specialized Research Fund for the Doctoral Program of Higher Education (20114407110009), and Hunan Provincial Innovation Foundation for Postgraduate under Grant (lx2009B120).
This paper was recommended for publication by Editor Bingyu ZHANG.
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Tang, Y., Chen, Y. Variational discretization for parabolic optimal control problems with control constraints. J Syst Sci Complex 25, 880–895 (2012). https://doi.org/10.1007/s11424-012-0279-y
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DOI: https://doi.org/10.1007/s11424-012-0279-y