Certified Reduced Basis Methods for Parametrized Partial Differential Equations [electronic resource] / by Jan S Hesthaven, Gianluigi Rozza, Benjamin Stamm.
Series: SpringerBriefs in MathematicsPublisher: Cham : Springer International Publishing : Imprint: Springer, 2016Edition: 1st ed. 2016Description: XIII, 131 p. 32 illus., 27 illus. in color. online resourceContent type:- text
- computer
- online resource
- 9783319224701
- Mathematics
- Partial differential equations
- Applied mathematics
- Engineering mathematics
- Computer mathematics
- Physics
- Mathematics
- Computational Mathematics and Numerical Analysis
- Partial Differential Equations
- Appl.Mathematics/Computational Methods of Engineering
- Theoretical, Mathematical and Computational Physics
- Applications of Mathematics
- 518 23
- QA71-90

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 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.