摘要
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 L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.
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 L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.
基金
Acknowledgments. The authors would like to thank the anonymous reviewers for their valu- able comments and suggestions on an earlier version of this paper. Tile first author was sup- ported by the National Natural Science Foundation of China （No. 11126086,11201485） and the F~mdamental Research Funds for the Central Universities （No.12CX04083A）
The second author was supported by the National Natural Science Foundation of China （No. 11171190）
The third author was supported by the National Natural Science Foundation of China （No.11101431）.
