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.

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
Mots clés : elliptic optimal control problem, state constraint, a priori error estimates
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     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},
     publisher = {EDP-Sciences},
     volume = {46},
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     zbl = {1271.65104},
     language = {en},
     url = {http://www.numdam.org/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. http://www.numdam.org/articles/10.1051/m2an/2011076/

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