TY - JOUR T1 - Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations AU - Sun , Tongjun AU - Ge , Liang AU - Liu , Wenbin JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 23 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/556.html KW - constrained optimal control problem, adaptive finite element approximation, equivalent a posteriori error estimates, parabolic equations, multi-meshes. AB -

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.