A priori error estimates of finite volume method for nonlinear optimal control problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 3, pp. 273-287
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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.
@article{SJVM_2017_20_3_a3,
author = {Z. Lu and L. Li and L. Cao and Ch. Hou},
title = {A priori error estimates of finite volume method for nonlinear optimal control problem},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {273--287},
publisher = {mathdoc},
volume = {20},
number = {3},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a3/}
}
TY - JOUR AU - Z. Lu AU - L. Li AU - L. Cao AU - Ch. Hou TI - A priori error estimates of finite volume method for nonlinear optimal control problem JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2017 SP - 273 EP - 287 VL - 20 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a3/ LA - ru ID - SJVM_2017_20_3_a3 ER -
%0 Journal Article %A Z. Lu %A L. Li %A L. Cao %A Ch. Hou %T A priori error estimates of finite volume method for nonlinear optimal control problem %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2017 %P 273-287 %V 20 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a3/ %G ru %F SJVM_2017_20_3_a3
Z. Lu; L. Li; L. Cao; Ch. Hou. A priori error estimates of finite volume method for nonlinear optimal control problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 3, pp. 273-287. http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a3/