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Dual weighted residual method for optimal control of hyperbolic equations of second order
Author(s) -
Kröner Axel
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110387
Subject(s) - discretization , residual , dual (grammatical number) , optimal control , a priori and a posteriori , mathematics , hyperbolic partial differential equation , method of mean weighted residuals , nonlinear system , state space , control (management) , control theory (sociology) , mathematical analysis , mathematical optimization , computer science , partial differential equation , algorithm , statistics , physics , art , philosophy , literature , epistemology , quantum mechanics , galerkin method , artificial intelligence
In this paper the dual weighted residual method for optimal control problems of hyperbolic equations of second order is considered. The state equation is written as a first order system in time and a posteriori error estimates separating the influences of time, space, and control discretization are derived to obtain a better accurancy of the discrete solution. A numerical example for optimal control of a nonlinear wave equation is presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)