Year: 2020
Author: Nikolaus von Daniels, Michael Hinze
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 14–40
Abstract
We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the adjoint equation, we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space. We prove a-priori estimates for the error between the discretized regularized problem and the limit problem. Since these estimates are not robust if the regularization parameter tends to zero, we establish robust estimates, which — depending on the problem's regularity — enhance the previous ones. In the special case of bang-bang solutions, these estimates are further improved. A numerical example confirms our analytical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1805-m2017-0171
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 14–40
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Optimal control Heat equation Control constraints Finite elements A-priori error estimates Bang-bang controls.