Double greedy algorithms: Reduced basis methods for transport dominated problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, p. 623-663
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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.

DOI : https://doi.org/10.1051/m2an/2013103
Classification:  65J10,  65N12,  65N15,  35B30
Keywords: tight surrogates, stable variational formulations, saddle point problems, double greedy schemes, greedy stabilization, rate-optimality, transport equations, convection-diffusion equations
@article{M2AN_2014__48_3_623_0,
     author = {Dahmen, Wolfgang and Plesken, Christian and Welper, Gerrit},
     title = {Double greedy algorithms: Reduced basis methods for transport dominated problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     pages = {623-663},
     doi = {10.1051/m2an/2013103},
     zbl = {1291.65339},
     mrnumber = {3177860},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_3_623_0}
}
Dahmen, Wolfgang; Plesken, Christian; Welper, Gerrit. Double greedy algorithms: Reduced basis methods for transport dominated problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, pp. 623-663. doi : 10.1051/m2an/2013103. http://www.numdam.org/item/M2AN_2014__48_3_623_0/

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