Geodesic
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/}
}
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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/