Optimal control of the convection-diffusion equation using stabilized finite element methods

In this paper we analyze the discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case...

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Published inNumerische Mathematik Vol. 106; no. 3; pp. 349 - 367
Main Authors Becker, Roland, Vexler, Boris
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.05.2007
Berlin Springer Nature B.V
New York, NY
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ISSN0029-599X
0945-3245
DOI10.1007/s00211-007-0067-0

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Summary:In this paper we analyze the discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches “optimize-then- discretize” and “discretize-then-optimize” coincide for the proposed discretization scheme. This allows for a symmetric optimality system at the discrete level and optimal order of convergence.
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ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-007-0067-0