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October 2011, 7(4): 927-945. doi: 10.3934/jimo.2011.7.927
Superconvergence property of finite element methods for parabolic optimal control problems
Chunjuan Hou 1, , Yanping Chen 2, and Zuliang Lu 3,
Huashang College Guangdong University Of Business Studies, Guangzhou 511300, China
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, China
Received October 2010 Revised June 2011 Published August 2011
In this paper, a finite element method for a parabolic optimal control problem is introduced and analyzed. For the discretization of a quadratic convex optimal control problem, the state and co-state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. As a result, it is proved in this paper that the difference between a suitable interpolation of the control and its finite element approximation has superconvergence property in order $O(h^2)$. Finally, two numerical examples are presented to confirm our theoretical results.
Keywords: superconvergence property., parabolic equation, finite element methods, Optimal control problems.
Mathematics Subject Classification: 49J20, 65N3.
Citation: Chunjuan Hou, Yanping Chen, Zuliang Lu. Superconvergence property of finite element methods for parabolic optimal control problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 927-945. doi: 10.3934/jimo.2011.7.927
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