357 | RWTH Publication No: 230477 2013   IGPM357.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) |