# Double greedy algorithms: Reduced basis methods for transport dominated problems

Wolfgang Dahmen; Christian Plesken; Gerrit Welper

- Volume: 48, Issue: 3, page 623-663
- ISSN: 0764-583X

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topDahmen, Wolfgang, Plesken, Christian, and Welper, Gerrit. "Double greedy algorithms: Reduced basis methods for transport dominated problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.3 (2014): 623-663. <http://eudml.org/doc/273103>.

@article{Dahmen2014,

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.},

author = {Dahmen, Wolfgang, Plesken, Christian, Welper, Gerrit},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {tight surrogates; stable variational formulations; saddle point problems; double greedy schemes; greedy stabilization; rate-optimality; transport equations; convection-diffusion equations},

language = {eng},

number = {3},

pages = {623-663},

publisher = {EDP-Sciences},

title = {Double greedy algorithms: Reduced basis methods for transport dominated problems},

url = {http://eudml.org/doc/273103},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Dahmen, Wolfgang

AU - Plesken, Christian

AU - Welper, Gerrit

TI - Double greedy algorithms: Reduced basis methods for transport dominated problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 3

SP - 623

EP - 663

AB - 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.

LA - eng

KW - tight surrogates; stable variational formulations; saddle point problems; double greedy schemes; greedy stabilization; rate-optimality; transport equations; convection-diffusion equations

UR - http://eudml.org/doc/273103

ER -

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