@Article{IJNAM-10-1,
author = {Tongjun, Sun and Liang, Ge and Wenbin, Liu},
title = {Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {1},
pages = {1--23},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2013-IJNAM-556},
url = {https://global-sci.com/article/83380/equivalent-a-posteriori-error-estimates-for-a-constrained-optimal-control-problem-governed-by-parabolic-equations}
}