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