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Journal of Numerical Mathematics

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

Managing Editor: Olshanskii, Maxim

Editorial Board: 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 14, Issue 1 (Mar 2006)


Distributed optimal control of lambda–omega systems

A. Borzì
  • Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, A–8010 Graz, Austria
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ R. Griesse
  • Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, A–4040 Linz, Austria
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

The formulation, analysis, and numerical solution of distributed optimal control problems governed by lambda–omega systems is presented. These systems provide a universal model for reaction-diffusion phenomena with turbulent behavior. Existence and regularity properties of solutions to the free and controlled lambda–omega models are investigated. To validate the ability of distributed control to drive lambda–omega systems from a chaotic to an ordered state, a space-time multigrid method is developed based on a new smoothing scheme. Convergence properties of the multigrid scheme are discussed and results of numerical experiments are reported.

Key Words: lambda–omega systems,; optimal control,; multigrid methods

About the article

Published in Print: 2006-03-01

Citation Information: Journal of Numerical Mathematics jnma, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/156939506776382120.

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