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
Access Full Article
top
Abstract
topHow to cite
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.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.