Reduced Basis Methods for Partial Differential Equations: An Introduction

by Alfio Quarteroni

1 Introduction.- 2 Representative analysis and (high-fidelity) approximation.- 3 Getting parameters into play.- 4 RB basic principle, basic properties.- 5 Construction of reduced basis spaces.- 6 Algebraic and geometrical structure.- 7 RB method in actions.- 8 Extension to nonaffine problems.- 9 Extension to nonlinear problems.- 10 Reduction and a natural interplay.- 11 Further extensions.- 12 Appendix A Elements of functional analysis.

312 pages, Paperback

First published July 27, 2015