Abstract
In this chapter we describe the basic ideas of reduced basis (RB) approximation methods for rapid and reliable evaluation of input-output relationships in which the output is expressed as a functional of a field variable that is the solution of an input-parametrized partial differential equation (PDE). We shall focus on linear output functionals and affinely parametrized linear elliptic coercive PDEs; however the methodology is much more generally applicable as we discuss in Sec. 18.6 at the end of this chapter. The combination with an efficient a posteriori error estimation is a key factor for RB methods to be computationally successful.
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© 2009 Springer-Verlag Italia, Milan
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(2009). Reduced basis approximation for parametrized partial differential equations. In: Numerical Models for Differential Problems. MS&A, vol 2. Springer, Milano. https://doi.org/10.1007/978-88-470-1071-0_18
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DOI: https://doi.org/10.1007/978-88-470-1071-0_18
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1070-3
Online ISBN: 978-88-470-1071-0
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