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  • © 2016

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

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  • 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

  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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USD 59.99
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  • ISBN: 978-3-319-22470-1
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  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book
USD 74.99
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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
  2. Introduction

    • Jan S. Hesthaven, Gianluigi Rozza, Benjamin Stamm
    Pages 1-13
  3. Parametrized Differential Equations

    • Jan S. Hesthaven, Gianluigi Rozza, Benjamin Stamm
    Pages 15-25
  4. Reduced Basis Methods

    • Jan S. Hesthaven, Gianluigi Rozza, Benjamin Stamm
    Pages 27-43
  5. Certified Error Control

    • Jan S. Hesthaven, Gianluigi Rozza, Benjamin Stamm
    Pages 45-66
  6. The Empirical Interpolation Method

    • Jan S. Hesthaven, Gianluigi Rozza, Benjamin Stamm
    Pages 67-85
  7. Beyond the Basics

    • Jan S. Hesthaven, Gianluigi Rozza, Benjamin Stamm
    Pages 87-118
  8. Back Matter

    Pages 119-131

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.

Keywords

  • Applied mathematics
  • Earth sciences
  • Empirical interpolation
  • PDE
  • Reduced basis methods
  • Time-dependent problems
  • partial differential equations

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)

Authors and Affiliations

  • EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne EPFL, Lausanne, Switzerland

    Jan S Hesthaven

  • SISSA MathLab, International School for Advanced Studies, Trieste, Italy

    Gianluigi Rozza

  • Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ Paris 06, CNRS, Paris Cedex 05, France

    Benjamin Stamm

Bibliographic Information

Buying options

eBook
USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-22470-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 74.99
Price excludes VAT (USA)