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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
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.
Keywords:Tight surrogates, stable variational formulations, saddle point problems, double greedy schemes, greedy stabilization, rate–optimality, transport equations, convection–diffusion equations.
DOI: 10.1051/m2an/2013103
Publication:Mathematical modelling and numerical analysis = Modélisation mathématique et analyse numérique
48(3), 623-663 (2014)