# A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD

Eileen Kammann; Fredi Tröltzsch; Stefan Volkwein

- Volume: 47, Issue: 2, page 555-581
- ISSN: 0764-583X

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topKammann, Eileen, Tröltzsch, Fredi, and Volkwein, Stefan. "A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 555-581. <http://eudml.org/doc/273256>.

@article{Kammann2013,

abstract = {We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). The distance between a local solution of the reduced problem to a local solution of the original problem is estimated.},

author = {Kammann, Eileen, Tröltzsch, Fredi, Volkwein, Stefan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {optimal control; semilinear partial differential equations; error estimation; proper orthogonal decomposition; semilinear parabolic equations},

language = {eng},

number = {2},

pages = {555-581},

publisher = {EDP-Sciences},

title = {A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD},

url = {http://eudml.org/doc/273256},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Kammann, Eileen

AU - Tröltzsch, Fredi

AU - Volkwein, Stefan

TI - A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 2

SP - 555

EP - 581

AB - We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). The distance between a local solution of the reduced problem to a local solution of the original problem is estimated.

LA - eng

KW - optimal control; semilinear partial differential equations; error estimation; proper orthogonal decomposition; semilinear parabolic equations

UR - http://eudml.org/doc/273256

ER -

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