Geodesic
$L^\infty$-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 91-105

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In this paper, we investigate $L^\infty$-error estimates for convex quadratic optimal control problems governed by nonlinear elliptic partial differential equations using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive $L^\infty$-error estimates of optimal order for a mixed finite element approximation of a semilinear elliptic optimal control problem. Finally, we present numerical tests which confirm our theoretical results. 
@article{SJVM_2009_12_1_a6,
     author = {Zuliang Lu and Yanping Chen},
     title = {$L^\infty$-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {91--105},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a6/}
}
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Zuliang Lu; Yanping Chen. $L^\infty$-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 91-105. http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a6/