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)
