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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Volume 22, Issue 1 (Mar 2014)

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A survey of numerical methods for convection–diffusion optimal control problems

Z. J. Zhou
  • Corresponding author
  • College of Mathematics Science, Shandong Normal University, 250014 Ji’nan, China and Bereich Optimierung und Approximation, Universit¨at Hamburg, Bundestrasse 55, 20146 Hamburg, Germany
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/ N.N. Yan
  • Corresponding author
  • LSEC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China
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Published Online: 2014-03-07 | DOI: https://doi.org/10.1515/jnum-2014-0003

Abstract

In this paper we present a survey of numericalmethods for optimal control problems governed by convection-diffusion equations. For ease of exposition we focus on stationary convection-diffusion optimal control problems with distributed control. Several effective numericalmethods including stabilizedmethods and discontinuous Galerkinmethods are reviewed. Furthermore, we also make some investigations about convection-diffusion optimal control problems with state constraints and pointwisely imposed control.

Keywords : convection-diffusion equations; optimal control problems; streamline upwind Petrov-Galerkin method; edge stabilization Galerkin method; local projection stabilization method; interior penalty discontinuous Galerkin method; local discontinuous Galerkin method; a priori error estimates; a posteriori error estimates; adaptive finite element method

About the article

Published Online: 2014-03-07

Published in Print: 2014-03-01


Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum-2014-0003.

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