TY - JOUR
T1 - A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems
AU - Hongfei Fu, Hongxing Rui & Hui Guo
JO - Journal of Computational Mathematics
VL - 1
SP - 88
EP - 106
PY - 2013
DA - 2013/02
SN - 31
DO - http://doi.org/10.4208/jcm.1210-m3966
UR - https://global-sci.org/intro/article_detail/jcm/9723.html
KW - Characteristic finite element method, Constrained optimal control, Convection-diffusion-reaction equations, Pointwise inequality constraints, A priori error estimates.
AB - <p style="text-align: justify;">In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts: The first part is about integration of the state over the whole time interval, the second part refers to final-time state, and the third part is a regularization term about the control. We discretize the state and co-state by piecewise linear continuous functions, while the control is approximated by piecewise constant functions. Pointwise inequality function constraints on the control are considered, and optimal a&nbsp; $L^2$-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.</p>