Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Jan S Hesthaven, Gianluigi Rozza, Benjamin Stamm (Autoren)

Buch | Softcover

XIII, 131 Seiten

2015 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-22469-5 (ISBN)

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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.

1 Introduction and Motivation.- 2 Parametrized Differential Equations.- 3 Reduced Basis Methods.- 4 Certified Error Control.- 5 The Empirical Interpolation Method.- 6 Beyond the Basics.- 7 Appendix A Mathematical Preliminaries.

"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)

Erscheint lt. Verlag	1.9.2015
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	XIII, 131 p. 32 illus., 27 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	249 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Applications of Mathematics • Applied mathematics • Computational Mathematics and Numerical Analysis • earth sciences • Empirical interpolation • mathematics and statistics • Partial differential equations • Partielle Differenzialgleichungen • PDE • Reduced basis methods • Time-dependent problems
ISBN-10	3-319-22469-7 / 3319224697
ISBN-13	978-3-319-22469-5 / 9783319224695
Zustand	Neuware