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Erschienen in:
2016 | OriginalPaper | Buchkapitel
The Theoretical Rationale Behind
verfasst von : Alfio Quarteroni, Andrea Manzoni, Federico Negri
Erschienen in: Reduced Basis Methods for Partial Differential Equations
Verlag: Springer International Publishing
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We discuss relevant theoretical features of the RB methods seen in the previous chapters. We specifically highlight those properties of the solution manifold that are directly inherited from the parametrized differential operators. We define the Kolmogorov
n
-width to measure how well suited
n
-dimensional subspaces are to approximate the solution manifold. At the end we show that a wise selection of snapshots yields exponential convergence when approximating the solution manifold. This key property, that warrants the computational efficiency of RB methods, is provided by greedy algorithms and POD techniques used to construct RB spaces that are introduced in the subsequent chapters.