A~posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 261-276
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This paper is aimed at studying finite element discretization for a class of quadratic boundary optimal control problems governed by nonlinear elliptic equations. We derive a posteriori error estimates for the coupled state and control approximation. Such estimates can be used to construct a reliable adaptive finite element approximation for the boundary optimal control problem. Finally, we present a numerical example to confirm our theoretical results.
@article{SJVM_2011_14_3_a2,
author = {Z. Lu},
title = {A~posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {261--276},
publisher = {mathdoc},
volume = {14},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a2/}
}
TY - JOUR AU - Z. Lu TI - A~posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2011 SP - 261 EP - 276 VL - 14 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a2/ LA - ru ID - SJVM_2011_14_3_a2 ER -
%0 Journal Article %A Z. Lu %T A~posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2011 %P 261-276 %V 14 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a2/ %G ru %F SJVM_2011_14_3_a2
Z. Lu. A~posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 261-276. http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a2/