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

Michael Hintermüller; Ronald H.W. Hoppe; Yuri Iliash; Michael Kieweg

ESAIM: Control, Optimisation and Calculus of Variations (2007)

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

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topHintermüller, 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 (2007): 540-560. <http://eudml.org/doc/90882>.

@article{Hintermüller2007,

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.
},

author = {Hintermüller, Michael, Hoppe, Ronald H.W., Iliash, Yuri, Kieweg, 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; a posteriori error analysis; distributed optimal control problems; adaptive finite element methods; data oscillations; numerical examples},

language = {eng},

month = {11},

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/90882},

volume = {14},

year = {2007},

}

TY - JOUR

AU - Hintermüller, Michael

AU - Hoppe, Ronald H.W.

AU - Iliash, Yuri

AU - Kieweg, 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

DA - 2007/11//

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; a posteriori error analysis; distributed optimal control problems; adaptive finite element methods; data oscillations; numerical examples

UR - http://eudml.org/doc/90882

ER -

## References

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