Double greedy algorithms: Reduced basis methods for transport dominated problems∗
Received: 21 February 2013
Revised: 28 June 2013
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.
Mathematics Subject Classification: 65J10 / 65N12 / 65N15 / 35B30
Key words: Tight surrogates / stable variational formulations / saddle point problems / double greedy schemes / greedy stabilization / rate-optimality / transport equations / convection-diffusion equations
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