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L∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem

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  • Lu, Zuliang
  • Zhang, Shuhua

Abstract

In this paper, we investigate L∞-error estimates of the bilinear elliptic optimal control problem by rectangular Raviart–Thomas mixed finite element methods. The control variable enters the state equation as a coefficient. The state and the co-state variables are approximated by the Raviart–Thomas mixed finite elements of order k=1, and the control variable is approximated by piecewise linear functions. The L∞-error estimates are obtained for the control variable and coupled state variable, and the convergence rates of orders O(h2) and O(h32|lnh|12) are also gained for the control and state variables and the flux of the state and co-state variables, respectively. In addition, the performance of the error estimates is assessed by two numerical examples.

Suggested Citation

  • Lu, Zuliang & Zhang, Shuhua, 2017. "L∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 79-94.
    • Handle: RePEc:eee:apmaco:v:300:y:2017:i:c:p:79-94
    DOI: 10.1016/j.amc.2016.12.006
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    Cited by:

    1. Zhang, Jun & Wang, JinRong, 2018. "Numerical analysis for Navier–Stokes equations with time fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 481-489.

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