A posteriori error estimates for optimal distributed control governed by the evolution equations
type: Item
instance of: scholarly article
title: A posteriori error estimates for optimal distributed control governed by the evolution equations
zbMATH Open document ID: 1208.65091
author: Chunguang Xiong
author: Yuan Li
published in: Applied Numerical Mathematics
publication date: 2011-01-21T00:00:00Z
review text: A posteriori error estimates are used to design adaptive grids for solving partial differential equation (PDEs) by finite elements. They are used often for optimal control problems (OPC's) with PDEs, whereas most of the recent work is concentrated on elliptic equations. The authors develop a posteriori error estimates by using space-time finite elements for optimal control problems with pure parabolic problems [as in the work of \textit{D. Meidner} and \textit{B. Vexler}, SIAM J. Control Optim. 46, No.~1, 116--142 (2007; Zbl 1149.65051)], diffusion-convection problems and hyperbolic problems. It would be interesting to apply these results to design efficient adaptive space-time finite elements for OPC's with evolutionary PDE's.
reviewed by: Bülent Karasözen
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 5840215
zbMATH Keywords: optimal control
zbMATH Keywords: evolution equations
zbMATH Keywords: space-time finite elements
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: method of lines
zbMATH Keywords: parabolic problems
MaRDI profile type: Publication
full work available at URL: j.apnum.2010.09.004
OpenAlex ID: W2059224416
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DOI: 10.1016/J.APNUM.2010.09.004
description: scientific article; zbMATH DE number 5840215