|Preprint-No.:||< 357 >||Published in:||February 2013||PDF-File:||IGPM357_k.pdf|
|Title:||Double Greedy Algorithms: Reduced Basis Methods for Transport Dominated Problems|
|Authors:||Wolfgang Dahmen, Christian Plesken, Gerrit Welper|
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.
|Keywords:||Tight surrogates, stable variational formulations, saddle point problems, double greedy schemes, greedy stabilization, rate–optimality, transport equations, convection–diffusion equations.|
|Publication:||Mathematical modelling and numerical analysis = Modélisation mathématique et analyse numérique |
48(3), 623-663 (2014)