This article is cited in 1 paper

A priori error estimates of finite volume method for nonlinear optimal control problem

Z. Lu^ab, L. Li^a, L. Cao^a, Ch. Hou<sup>c

a</sup> Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Chongqing, 404000, P.R. China
^b Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin, 300222, P.R. China
^c Huashang College Guangdong University of Finance, Guangzhou, 511300, P.R. China

Abstract: In this paper, we study a priori error estimates for a finite volume element approximation of a nonlinear optimal control problem. The schemes use discretizations base on a finite volume method. For the variational inequality, we use a method of the variational discretization concept to obtain the control. Under some reasonable assumptions, we obtain some optimal order error estimates. The approximate order for the state, costate, and control variables is $O(h^2)$ or $O(h^2\sqrt{|\ln h|})$ in the sense of $L^2$-norm or $L^\infty$-norm. A numerical experiment is presented to test the theoretical results. Finally, we give some conclusions and future works.

Key words: a priori error estimates, nonlinear optimal control problem, finite volume method, variational discretization.

MSC: 49J20, 65N30

Received: 08.12.2016
Revised: 04.03.2017

DOI: 10.15372/SJNM20170304

 English version: Numerical Analysis and Applications, 2017, 10:3, 224–236

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