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.
Author(s): Jan S Hesthaven, Gianluigi Rozza, Benjamin Stamm (auth.)
Series: SpringerBriefs in Mathematics
Edition: 1
Publisher: Springer International Publishing
Year: 2016
Language: English
Pages: XIII, 131
Tags: Computational Mathematics and Numerical Analysis; Partial Differential Equations; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
Front Matter....Pages i-xiii
Introduction....Pages 1-13
Parametrized Differential Equations....Pages 15-25
Reduced Basis Methods....Pages 27-43
Certified Error Control....Pages 45-66
The Empirical Interpolation Method....Pages 67-85
Beyond the Basics....Pages 87-118
Back Matter....Pages 119-131
