Variational discretization for parabolic optimal control problems with control constraints |
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Authors: | Yuelong Tang Yanping Chen |
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Affiliation: | 1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China 2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China
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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 $left| {left| {u - U_h } right|} right|_{L^infty left( {J;L^2 left( Omega right)} right)} = Oleft( {h^2 + k} right)$ . It is much better than a priori error estimates of standard finite element and backward Euler method where $left| {left| {u - U_h } right|} right|_{L^infty left( {J;L^2 left( Omega right)} right)} = Oleft( {h + k} right)$ . 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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