DOUBLE GREEDY ALGORITHMS: REDUCED BASIS METHODS FOR TRANSPORT DOMINATED PROBLEMS

作者：Dahmen Wolfgang^*; Plesken Christian; Welper Gerrit

来源：Esaim: Mathematical Modelling and Numerical Analysis , 2014, 48(3): 623-663.

DOI：10.1051/m2an/2013103

• Tight surrogates
• stable variational formulations
• saddle point problems
• double greedy schemes
• greedy stabilization
• rate-optimality
• transport equations
• convection-diffusion equations

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.

• 出版日期2014-5