Volume 46, Number 5, September-October 2012
|Page(s)||1107 - 1120|
|Published online||13 February 2012|
A priori error estimates for a state-constrained elliptic optimal control problem
Universität Duisburg-Essen, Fakultät für Mathematik, Forsthausweg 2,
2 Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Revised: 5 October 2011
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.
Mathematics Subject Classification: 49J20 / 35B45
Key words: Elliptic optimal control problem / state constraint / a priori error estimates
© EDP Sciences, SMAI, 2012
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