Double greedy algorithms: Reduced basis methods for transport dominated problems∗. (20th January 2014)

• Record Type: Journal Article
• Authors: Dahmen, Wolfgang; Plesken, Christian; Welper, Gerrit
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 3(2014)
• Page Start: 623
• Page End: 663
• Publication Date: 2014-01-20
• Subjects: Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2013103
• Languages: English
• ISSNs: 0764-583X

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov <italic>n</italic>-widths of the solution sets. The central ingredient is the construction of computationally feasible "tight" surrogates which in turn are based on deriving a suitable well-conditioned variational formulation for the parameter dependent problem. The theoretical results are illustrated by numerical experiments for convection-diffusion and pure transport equations. In particular, the latter example sheds some light on the smoothness of the dependence of the solutions on the parameters.</p> </abstract>