A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type

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.