@Article{IJNAM-10-1, author = {Sun , TongjunGe , Liang and Liu , Wenbin}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/556.html} }