Double greedy algorithms: Reduced basis methods for transport dominated problems∗. (20th January 2014) - Dahmen, Wolfgang; Plesken, Christian; Welper, Gerrit
<x content-type="archive" xml:space="preserve">Abstract</x> 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.