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

Zuliang Lu and Shuhua Zhang

Applied Mathematics and Computation, 2017, vol. 300, issue C, 79-94

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.

Keywords: Bilinear optimal control problem; Raviart–Thomas mixed finite element methods; Rectangular partition; L∞-error estimates (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:300:y:2017:i:c:p:79-94

DOI: 10.1016/j.amc.2016.12.006

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