A posteriori error estimates for optimal control problems constrained by convection-diffusion equations

作者：Fu, Hongfei^*; Rui, Hongxing; Zhou, Zhaojie

来源：Frontiers of Mathematics in China, 2016, 11(1): 55-75.

DOI：10.1007/s11464-015-0456-0

• Optimal control problem
• characteristic finite element
• convection-diffusion equation
• multi-set adaptive meshes
• a posterior error estimate

We propose a characteristic finite element discretization of evolutionary type convection-diffusion optimal control problems. Nondivergence-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.

• 出版日期2016-2
• 单位山东师范大学; 山东大学; 中国石油大学（北京）