# An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Kieweg; Yuri Iliash^{[1]}; Ronald H. W. Hoppe; Michael Hintermüller

- [1] Institute of Mathematics, University of Augsburg, 86159 Augsburg, Germany;

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 3, page 540-560
- ISSN: 1292-8119

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topKieweg, Michael, et al. "An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2008): 540-560. <http://eudml.org/doc/245330>.

@article{Kieweg2008,

abstract = {We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide a bulk criterion for mesh refinement that also takes into account data oscillations and is realized by a greedy algorithm. A detailed documentation of numerical results for selected test problems illustrates the convergence of the adaptive finite element method.},

affiliation = {Institute of Mathematics, University of Augsburg, 86159 Augsburg, Germany;},

author = {Kieweg, Michael, Iliash, Yuri, Hoppe, Ronald H. W., Hintermüller, Michael},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {a posteriori error analysis; distributed optimal control problems; control constraints; adaptive finite element methods; residual-type a posteriori error estimators; data oscillations; numerical examples},

language = {eng},

number = {3},

pages = {540-560},

publisher = {EDP-Sciences},

title = {An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints},

url = {http://eudml.org/doc/245330},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Kieweg, Michael

AU - Iliash, Yuri

AU - Hoppe, Ronald H. W.

AU - Hintermüller, Michael

TI - An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2008

PB - EDP-Sciences

VL - 14

IS - 3

SP - 540

EP - 560

AB - We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide a bulk criterion for mesh refinement that also takes into account data oscillations and is realized by a greedy algorithm. A detailed documentation of numerical results for selected test problems illustrates the convergence of the adaptive finite element method.

LA - eng

KW - a posteriori error analysis; distributed optimal control problems; control constraints; adaptive finite element methods; residual-type a posteriori error estimators; data oscillations; numerical examples

UR - http://eudml.org/doc/245330

ER -

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