Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations
type: Item
instance of: scholarly article
title: Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations
zbMATH Open document ID: 1412.65228
author: H. Yücel
author: Martin Stoll
author: P. Benner
publication date: 2019-02-05T00:00:00Z
full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol48/abstract.php
review text: The authors study a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection-diffusion equation. The authors apply the symmetric interior penalty Galerkin method for the diffusion and the upwind discretization for the convection in order to discretize the optimization problem in space. The semi-smooth Newton method and the Moreau-Yosida regularization method are introduced to solve the optimality system. Some residual-based error estimators are also proposed for both approaches. Numerical examples are given to demonstrate the performance of the proposed error estimators.
reviewed by: Li-Jun Yi
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 7012416
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: convection-diffusion equations
zbMATH Keywords: optimal control problem
zbMATH Keywords: a posteriori error estimate
MaRDI profile type: Publication
OpenAlex ID: W2901892263
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Wikidata QID: Q128881673
DOI: 10.1553/ETNA_VOL48S407
published in: ETNA - Electronic Transactions on Numerical Analysis