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A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints

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Abstract

In this paper, we propose a mixed variational scheme for optimal control problems with point-wise state constraints, the main idea is to reformulate the optimal control problems to a constrained minimization problem involving only the state, which is characterized by a fourth order variational inequality. Then mixed form based on this fourth order variational inequality is formulated and a direct numerical algorithm is proposed without the optimality conditions of underlying optimal control problems. The a priori and a posteriori error estimates are proved for the mixed finite element scheme. Numerical experiments confirm the efficiency of the new strategy.

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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wei Gong

  2. LSEC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ningning Yan

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  1. Wei Gong
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  2. Ningning Yan
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Correspondence to Wei Gong.

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Gong, W., Yan, N. A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints. J Sci Comput 46, 182–203 (2011). https://doi.org/10.1007/s10915-010-9392-z

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  • DOI: https://doi.org/10.1007/s10915-010-9392-z

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