New a posteriori error estimates of mixed finite element methods for quadratic optimal control problems governed by semilinear parabolic equations with integral constraint

被引：0
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作者：
Zuliang Lu
Shaohong Du
Yuelong Tang
机构：
[1] Chongqing Three Gorges University,School of Mathematics and Statistics
[2] Beijing Computational Science Research Center,Laboratory for Applied Mathematics
[3] Chongqing Jiaotong University,School of Science
[4] Hunan University of Science and Engineering,Department of Mathematics and Computational Science
来源：
Boundary Value Problems | / 2013卷
关键词：
error estimates; quadratic optimal control problems; semilinear parabolic equations; mixed finite element methods; integral constraint;
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摘要：
In this paper, we investigate new L∞(L2) and L2(L2)-posteriori error estimates of mixed finite element solutions for quadratic optimal control problems governed by semilinear parabolic equations. The state and the co-state are discretized by the order one Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in L∞(J;L2(Ω))-norm and L2(J;L2(Ω))-norm for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the optimal control problem.
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