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Superconvergence analysis and a posteriori error estimation of a finite element method for an optimal control problem governed by integral equations

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Abstract

In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type a posteriori error estimator is provided, which can be used for adaptive mesh refinement.

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Authors and Affiliations

  1. LSEC, Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, P.R.China

    Ningning Yan

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  1. Ningning Yan
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Correspondence to Ningning Yan.

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Dedicated to Ivan Hlaváček on the occasion of his 75th birthday

The research project is supported by the National Basic Research Program under the Grant 2005CB321701 and the National Natural Science Foundation of China under the Grant 10771211.

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Yan, N. Superconvergence analysis and a posteriori error estimation of a finite element method for an optimal control problem governed by integral equations. Appl Math 54, 267–283 (2009). https://doi.org/10.1007/s10492-009-0017-5

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