Numerical Approximation of Exact Controls for Waves
This book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is accomplished in the abstract functional setting of conservative semigroups.The main results of the work u...
Enregistré dans:
| Auteurs principaux: | , |
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| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Udgivelse: | 1st ed. 2013. |
| Serier: | SpringerBriefs in Mathematics
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| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Numerical approximation of exact controls for waves, Sylvain Ervedoza, Enrique Zuazua, 2013, New York, Springer, BCAM, 1 vol. (XVII-122 p.), SpringerBriefs in Mathematics / BCAM, 978-1-4614-5807-4 • Numerical approximation of exact controls for waves, Sylvain Ervedoza, Enrique Zuazua, 2013, New York, Springer, BCAM, 1 vol. (XVII-122 p.), SpringerBriefs in Mathematics / BCAM, 978-1-4614-5807-4 • Numerical Approximation of Exact Controls for Waves, Texte imprimé, 9781461458098 |
| Summary: | This book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is accomplished in the abstract functional setting of conservative semigroups.The main results of the work unify, to a large extent, these two approaches, which yield similaralgorithms and convergence rates. The discrete approach, however, gives not only efficient numerical approximations of the continuous controls, but also ensures some partial controllability properties of the finite-dimensional approximated dynamics. Moreover, it has the advantage of leading to iterative approximation processes that converge without a limiting threshold in the number of iterations. Such a threshold, which is hard to compute and estimate in practice, is a drawback of the methods emanating from the continuous approach. To complement this theory, the book provides convergence results for the discrete wave equation when discretized using finite differences and proves the convergence of the discrete wave equation with non-homogeneous Dirichlet conditions. The first book to explore these topics in depth, "On the Numerical Approximations of Controls for Waves" has rich applications to data assimilation problems and will be of interest to researchers who deal with wave approximations. |
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| Emne beskrivelse: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9781461458081 |
| ISSN: | 2191-8201 |
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