New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems

被引：0
作者：
Zuliang Lu
Hongyan Liu
Chunjuan Hou
Longzhou Cao
机构：
[1] Chongqing Three Gorges University,Key Laboratory of Signal and Information Processing
[2] Chongqing Three Gorges University,Key Laboratory for Nonlinear Science and System Structure
[3] Tianjin University of Finance and Economics,Research Center for Mathematics and Economics
[4] Chongqing Wanzhou Long Bao Middle School,Huashang College
[5] Guangdong University of Finance,undefined
来源：
Journal of Inequalities and Applications | / 2016卷
关键词：
residual-based ; error estimates; nonlinear parabolic optimal control problems; version of finite element method; 49J20; 65N30;
D O I：
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摘要：
In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuous Galerkin finite element approximation for the control variable, we derive hp residual-based a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct a reliable hp adaptive finite element approximation for the nonlinear parabolic optimal control problems.
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