摘要
We propose a characteristic finite element evolutionary type convection-diffusion optimal control discretization of problems. Non- divergence-free velocity fields and bilateral inequality control constraints are handled. Then some residual type a posteriori error estimates are analyzed for the approximations of the control, the state, and the adjoint state. Based on the derived error estimators, we use them as error indicators in developing efficient multi-set adaptive meshes characteristic finite element algorithm for such optimal control problems. Finally, one numerical example is given to check the feasibility and validity of multi-set adaptive meshes refinements.
We propose a characteristic finite element evolutionary type convection-diffusion optimal control discretization of problems. Non- divergence-free velocity fields and bilateral inequality control constraints are handled. Then some residual type a posteriori error estimates are analyzed for the approximations of the control, the state, and the adjoint state. Based on the derived error estimators, we use them as error indicators in developing efficient multi-set adaptive meshes characteristic finite element algorithm for such optimal control problems. Finally, one numerical example is given to check the feasibility and validity of multi-set adaptive meshes refinements.
基金
The authors would like to thank tile anonymous referees for their valuable comments and suggestions on an earlier version of this paper. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11201485, 11171190, 11301311）, the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province （No. BS2013NJ001）, and tile Fundamental Research Funds for the Central Universities （Nos. 14CX02217A, 14CX02144A）.
