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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...
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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