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

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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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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, China

    Hongfei Fu

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Hongxing Rui

  3. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China

    Zhaojie Zhou

Authors
  1. Hongfei Fu
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  2. Hongxing Rui
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  3. Zhaojie Zhou
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Correspondence to Hongfei Fu.

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Fu, H., Rui, H. & Zhou, Z. A posteriori error estimates for optimal control problems constrained by convection-diffusion equations. Front. Math. China 11, 55–75 (2016). https://doi.org/10.1007/s11464-015-0456-0

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  • DOI: https://doi.org/10.1007/s11464-015-0456-0

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