Certified Reduced Basis Methods for Parametrized Partial Differential Equations

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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.

 

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Contents

1 Introduction
1
2 Parametrized Differential Equations
14
3 Reduced Basis Methods
27
4 Certified Error Control
44
5 The Empirical Interpolation Method
67
6 Beyond the Basics
87
Appendix A Mathematical Preliminaries
119
Index
129
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