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Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines

Author

Listed:
  • Madiha Sana

    (Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
    These authors contributed equally to this work.)

  • Muhammad Mustahsan

    (Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
    These authors contributed equally to this work.)

Abstract

In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.

Suggested Citation

  • Madiha Sana & Muhammad Mustahsan, 2019. "Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines," Mathematics, MDPI, vol. 7(5), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:452-:d:232750
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    References listed on IDEAS

    as
    1. Dorota Jasińska & Dorota Kropiowska, 2018. "The Optimal Design of an Arch Girder of Variable Curvature and Stiffness by Means of Control Theory," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-13, December.
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    Cited by:

    1. Dawei An & Weiqing Huang & Weiquan Liu & Jinrui Xiao & Xiaochu Liu & Zhongwei Liang, 2021. "Meshing Drive Mechanism of Double Traveling Waves for Rotary Piezoelectric Motors," Mathematics, MDPI, vol. 9(4), pages 1-17, February.

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