A posteriori error estimates for optimal control problems constrained by convection-diffusion equations |
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Authors: | Hongfei Fu Hongxing Rui Zhaojie Zhou |
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Affiliation: | 1. College of Science, China University of Petroleum, Qingdao 266580, China2. School of Mathematics, Shandong University, Jinan 250100, China3. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China |
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Abstract: | 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. |
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Keywords: | Optimal control problem characteristic finite element convectiondiffusion equation multi-set adaptive meshes a posterior error estimate |
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