SpringerBriefs in Mathematics

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Authors: Hesthaven, Jan S, Rozza, Gianluigi, Stamm, Benjamin

  • The first book to introduce certified reduced basis methods for parametrized partial differentiation equations
  • Unique focus on both the mathematical aspects and algorithmic elements of the methods
  • Essential examples provide a point of departure for the development of more advanced applications
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Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-22470-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-22469-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Reviews

“This book provides comprehensive coverage of major aspects of the RB method, from derivation, analysis and implementation of the method to simulation of application problems. … an introduction to this emerging field for a general audience interested in scientific computing.” (Mario Ohlberger, Mathematical Reviews, December, 2016) 

“This book fills an important gap in the literature. It is an excellent starting point for young scholars approaching this new world, since it gives a well-balanced combination of theoretical aspects, practical details, and examples. … It also gives a nice picture of the research in this field, particularly in the last two chapters which address advanced (yet crucial) topics.” (Alessandro Veneziani, SIAM Review, Vol. 59 (1), 2016)


Table of contents (6 chapters)

  • Introduction

    Hesthaven, Jan S. (et al.)

    Pages 1-13

  • Parametrized Differential Equations

    Hesthaven, Jan S. (et al.)

    Pages 15-25

  • Reduced Basis Methods

    Hesthaven, Jan S. (et al.)

    Pages 27-43

  • Certified Error Control

    Hesthaven, Jan S. (et al.)

    Pages 45-66

  • The Empirical Interpolation Method

    Hesthaven, Jan S. (et al.)

    Pages 67-85

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-22470-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-22469-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Certified Reduced Basis Methods for Parametrized Partial Differential Equations
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-22470-1
DOI
10.1007/978-3-319-22470-1
Softcover ISBN
978-3-319-22469-5
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIII, 131
Number of Illustrations and Tables
5 b/w illustrations, 27 illustrations in colour
Topics