Sobolev gradients and differential equations
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete ve...
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| Hlavní autor: | |
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| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Vydání: | 2nd edition. |
| Edice: | Lecture Notes in Mathematics
1670 |
| Témata: | |
| On-line přístup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Poznámka: |
L'impression du document génère 280 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Version électronique de la seconde édition datant de 2010 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Sobolev gradients and differential equations, J. W. Neuberger, 2nd edition, 2010, Berlin, Springer, 1 vol. (XIII-289 p.), Lecture notes in mathematics, 978-3-642-04040-5 |
| Shrnutí: | A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations |
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| Popis jednotky: | L'impression du document génère 280 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Version électronique de la seconde édition datant de 2010 |
| Bibliografie: | Bibliogr. Index |
| ISBN: | 9783642040412 |
| ISSN: | 1617-9692 |
| Přístup: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |