Hesthaven Jan S, Rozza G., Stamm B. Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Springer International Publishing AG, Switzerland, 2016. – 139 p. – ISBN10: 3319224697The 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
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.
Topics
Computational Mathematics and Numerical Analysis
Partial Differential Equations
Appl. Mathematics / Computational Methods of Engineering
Theoretical, Mathematical and Computational Physics
Applications of MathematicsParametrized Differential Equations
Reduced Basis Methods
Certified Error Control
The Empirical Interpolation Method
Beyond the Basics
Appendix. Mathematical Preliminaries