A priori error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch; Simeon Steinig

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 5, page 1107-1120
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Rösch, Arnd, and Steinig, Simeon. "A priori error estimates for a state-constrained elliptic optimal control problem." ESAIM: Mathematical Modelling and Numerical Analysis 46.5 (2012): 1107-1120. <http://eudml.org/doc/277841>.

@article{Rösch2012,
abstract = {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.},
author = {Rösch, Arnd, Steinig, Simeon},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Elliptic optimal control problem; state constraint; a priori error estimates; elliptic control problem; state constrained; a priori error estimates; convergence rate; finite elements},
language = {eng},
month = {2},
number = {5},
pages = {1107-1120},
publisher = {EDP Sciences},
title = {A priori error estimates for a state-constrained elliptic optimal control problem},
url = {http://eudml.org/doc/277841},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Rösch, Arnd
AU - Steinig, Simeon
TI - A priori error estimates for a state-constrained elliptic optimal control problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 5
SP - 1107
EP - 1120
AB - 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.
LA - eng
KW - Elliptic optimal control problem; state constraint; a priori error estimates; elliptic control problem; state constrained; a priori error estimates; convergence rate; finite elements
UR - http://eudml.org/doc/277841
ER -

References

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