# Error estimates for finite element approximations of elliptic control problems

Walter Alt; Nils Bräutigam; Arnd Rösch

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

- Volume: 27, Issue: 1, page 7-22
- ISSN: 1509-9407

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topWalter Alt, Nils Bräutigam, and Arnd Rösch. "Error estimates for finite element approximations of elliptic control problems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.1 (2007): 7-22. <http://eudml.org/doc/271155>.

@article{WalterAlt2007,

abstract = {We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.},

author = {Walter Alt, Nils Bräutigam, Arnd Rösch},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {Linear quadratic optimal control problems; elliptic equations; finite element approximations; error estimates; linear quadratic optimal control problems},

language = {eng},

number = {1},

pages = {7-22},

title = {Error estimates for finite element approximations of elliptic control problems},

url = {http://eudml.org/doc/271155},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Walter Alt

AU - Nils Bräutigam

AU - Arnd Rösch

TI - Error estimates for finite element approximations of elliptic control problems

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2007

VL - 27

IS - 1

SP - 7

EP - 22

AB - We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

LA - eng

KW - Linear quadratic optimal control problems; elliptic equations; finite element approximations; error estimates; linear quadratic optimal control problems

UR - http://eudml.org/doc/271155

ER -

## References

top- [1] J.P. Aubin, Behaviour of the error of the approximate solution of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods, Ann. Scoula Norm. Sup. Pisa 21 (1967), 599-637. Zbl0276.65052
- [2] N. Bräutigam, Diskretisierung elliptischer Steuerungsprobleme, Ph.D. Thesis, Jena 2006.
- [3] N. Bräutigam, Discretization of Elliptic Control Problems by Finite Elements, Technical Report, Jena 2006.
- [4] P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland 1987.
- [5] C. Groß mann and H.-G. Roos, Numerik partieller Differentialgleichungen, Teubner 2005.
- [6] M. Hinze, A Variational Discretization Concept in Control Constrained Optimization: The Linear-Quadratic Case, Computational Optimization and Applications 30 (2005), 45-61. Zbl1074.65069
- [7] K. Malanowski, Convergence of Approximations vs. Regularity of Solutions for Convex, Control-Constrained Optimal Control Problems, Appl. Math. Optim. 8 (1981), 69-95. Zbl0479.49017
- [8] C. Meyer and A. Rösch, Superconvergence Properties of Optimal Control Problems, SIAM J. Contr. Opt. 43 (2004), 970-985. Zbl1071.49023
- [9] J.A. Nitsche, Ein Kriterium für die Quasioptimalität des Ritzschen Verfahrens, Numerische Mathematk 11 (1968), 346-348. Zbl0175.45801
- [10] B. Sendov and V.A. Popov, The Averaged Moduli of Smoothness, Wiley-Interscience 1988. Zbl0653.65002
- [11] F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen, Vieweg 2005.

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