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Convergence Rates of the POD–Greedy Method

Bernard Haasdonk — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, convergence rate statements for this algorithm have been given (Buffa 2009, Binev 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy algorithm (Haasdonk...

Reduced basis method for finite volume approximations of parametrized linear evolution equations

Bernard Haasdonk;  Mario Ohlberger — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

The model order reduction methodology of techniques offers efficient treatment of parametrized partial differential equations (PDEs) by providing both approximate solution procedures and efficient error estimates. RB-methods have so far mainly been applied to finite element schemes for elliptic and parabolic problems. In the current study we extend the methodology to general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations. The new theoretic...

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