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Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems |
Yuelong TANG1, Yanping CHEN2( ) |
| 1. Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, China; 2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
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Abstract We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results.
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| Keywords
Superconvergence property
quadratic optimal control problem
fully discrete finite element approximation
semilinear parabolic equation
interpolate operator
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Corresponding Author(s):
CHEN Yanping,Email:yanpingchen@scnu.edu.cn
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Issue Date: 01 April 2013
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