A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 4 : pp. 471–487
Abstract
In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal $L^2$-norm error estimates and the almost optimal $L^\infty$-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-8638
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 4 : pp. 471–487
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Bilinear control problem Finite element approximation Superconvergence A priori error estimate A posteriori error estimator.