A priori error estimates for a state-constrained elliptic optimal control problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, p. 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 : https://doi.org/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 = {A priori error estimates for a state-constrained elliptic optimal control problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {5},
     year = {2012},
     pages = {1107-1120},
     doi = {10.1051/m2an/2011076},
     zbl = {1271.65104},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2012__46_5_1107_0}
}
Rösch, Arnd; Steinig, Simeon. A priori error estimates for a state-constrained elliptic optimal control problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, pp. 1107-1120. doi : 10.1051/m2an/2011076. http://www.numdam.org/item/M2AN_2012__46_5_1107_0/

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