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Double greedy algorithms: Reduced basis methods for transport dominated problems ∗
Wolfgang Dahmen, Christian Plesken, Gerrit Welper
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 3 / May 2014

Published online by Cambridge University Press:

20 January 2014, pp. 623-663

Print publication:

May 2014
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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.

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

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

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