Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations
Year: 2013
Author: Tongjun Sun, Liang Ge, Wenbin Liu
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 1 : pp. 1–23
Abstract
In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic equations on multi-meshes. The control constraint is given in an integral sense: $K = \{u(t) ∈ L^2( Ω) : a ≤ ∫_ Ω u(t) ≤ b\}$. We derive equivalent a posteriori error estimates with lower and upper bounds for both the state and the control approximation, which are used as indicators in adaptive multi-meshes finite element scheme. The error estimates are then implemented and tested with promising numerical experiments.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-556
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 1 : pp. 1–23
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: constrained optimal control problem adaptive finite element approximation equivalent a posteriori error estimates parabolic equations multi-meshes.