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.

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

Inhalt

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.