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arXiv · 1302.5072

Double Greedy Algorithms: Reduced Basis Methods for Transport Dominated Problems

Wolfgang Dahmen·Christian Plesken·Gerrit Welper
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Abstract

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 $n$-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.

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BibTeXRIS

Wolfgang Dahmen, Christian Plesken, Gerrit Welper. 2013-02-20. Double Greedy Algorithms: Reduced Basis Methods for Transport Dominated Problems. https://doi.org/10.1051/m2an/2013103

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