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Superconvergence of Semidiscrete Splitting Positive Definite Mixed Finite Elements for Hyperbolic Optimal Control Problems

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  • Yuchun Hua
  • Yuelong Tang
  • Leopoldo Greco

Abstract

In this paper, we consider semidiscrete splitting positive definite mixed finite element methods for optimal control problems governed by hyperbolic equations with integral constraints. The state and costate are approximated by the lowest order Raviart-Thomas mixed rectangular finite element, and the control is approximated by piecewise constant functions. We derive some convergence and superconvergence results for the control, the state and the adjoint state. A numerical example is provided to demonstrate our theoretical results.

Suggested Citation

  • Yuchun Hua & Yuelong Tang & Leopoldo Greco, 2022. "Superconvergence of Semidiscrete Splitting Positive Definite Mixed Finite Elements for Hyperbolic Optimal Control Problems," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-10, January.
    • Handle: RePEc:hin:jnlamp:3520668
    DOI: 10.1155/2022/3520668
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