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Discontinuous Galerkin approximations for an optimal control problem of three-dimensional Navier–Stokes–Voigt equations

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Abstract

We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional Navier–Stokes–Voigt equations with a quadratic objective functional and box control constraints. The space-time error estimates of order \(O(\sqrt{\tau }+h)\), where \(\tau \) and h are respectively the time and space discretization parameters, are proved for the difference between the locally optimal controls and their discrete approximations.

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Acknowledgements

The authors would like to thank the reviewers for the helpful comments and suggestions, which improved the presentation of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2018.303.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Cung The Anh

  2. Department of Mathematics, Thang Long University, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Tran Minh Nguyet

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  1. Cung The Anh
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  2. Tran Minh Nguyet
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Correspondence to Cung The Anh.

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Anh, C.T., Nguyet, T.M. Discontinuous Galerkin approximations for an optimal control problem of three-dimensional Navier–Stokes–Voigt equations. Numer. Math. 145, 727–769 (2020). https://doi.org/10.1007/s00211-020-01132-0

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  • DOI: https://doi.org/10.1007/s00211-020-01132-0

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