A posteriori error estimates for hp finite element solutions of convex optimal control problems |
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| Authors: | Yanping Chen Yijie Lin |
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| Institution: | a School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, PR Chinab Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, PR China |
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| Abstract: | In this paper, we present a posteriori error analysis for hp finite element approximation of convex optimal control problems. We derive a new quasi-interpolation operator of Clément type and a new quasi-interpolation operator of Scott-Zhang type that preserves homogeneous boundary condition. The Scott-Zhang type quasi-interpolation is suitable for an application in bounding the errors in L2-norm. Then hp a posteriori error estimators are obtained for the coupled state and control approximations. Such estimators can be used to construct reliable adaptive finite elements for the control problems. |
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| Keywords: | 49J20 65N30 |
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