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 - <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>