Frontiers of Mathematics in China >
A posteriori error estimates for optimal control problems constrained by convection-diffusion equations
Received date: 23 Oct 2014
Accepted date: 28 Nov 2014
Published date: 02 Dec 2015
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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.
Hongfei FU , Hongxing RUI , Zhaojie ZHOU . A posteriori error estimates for optimal control problems constrained by convection-diffusion equations[J]. Frontiers of Mathematics in China, 2016 , 11(1) : 55 -75 . DOI: 10.1007/s11464-015-0456-0
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