Geodesic
A priori error estimates for a state-constrained elliptic optimal control problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 1107-1120 Cet article a éte moissonné depuis la source Numdam

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We examine an elliptic optimal control problem with control and state constraints in ℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 - ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

DOI : 10.1051/m2an/2011076
Classification : 49J20, 35B45
Keywords: elliptic optimal control problem, state constraint, a priori error estimates 
@article{M2AN_2012__46_5_1107_0,
     author = {R\"osch, Arnd and Steinig, Simeon},
     title = {\protect\emph{A priori }error estimates for a state-constrained elliptic optimal control problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1107--1120},
     year = {2012},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {5},
     doi = {10.1051/m2an/2011076},
     zbl = {1271.65104},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011076/}
}
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Rösch, Arnd; Steinig, Simeon. A priori error estimates for a state-constrained elliptic optimal control problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 1107-1120. doi: 10.1051/m2an/2011076

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