A priori error estimates of finite volume method for nonlinear optimal control problem
Z. Lu1,2, L. Li1, L. Cao1, Ch. Hou3
1Chongqing Three Gorges University, Chongqing, 404000, P.R. China
2Tianjin University of Finance and Economics, Tianjin, 300222, P.R. China
3Guangdong University of Finance, Guangzhou, 511300, P.R. China
Keywords: априорные оценки ошибки, нелинейная задача оптимального управления, метод конечных объемов, вариационная дискретизация, a priori error estimates, nonlinear optimal control problem, finite volume method, variational discretization
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 Oh2) or O(h2√|lnh|) in the sense of L2-norm or L∞-norm. A numerical experiment is presented to test the theoretical results. Finally, we give some conclusions and future works.
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