Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations

Haasdonk B, Ohlberger M

Research article (journal)

Abstract

The model order reduction methodology of reduced basis (RB) techniques offers efficienttreatment of parametrized partial differential equations (P2DEs) by providing both approximatesolution procedures and efficient error estimates. RB-methods have so far mainly been appliedto finite element schemes for elliptic and parabolic problems. In the current study we extend themethodology to general evolution schemes such as finite volume schemes for parabolic and hyperbolicevolution equations. The new theoretic contributions are the formulation of a reducedbasis approximation scheme for general evolution problems and the derivation of rigorous aposteriorierror estimates in various norms. Algorithmically, an offline/online decomposition ofthe scheme and the error estimators is realized. This is the basis for a rapid online computationin case of multiple-simulation requests. We introduce a new offline basis-generation algorithmbased on our a posteriori error estimator which combines ideas from existing approaches. Numericalexperiments for an instationary convection-diffusion problem demonstrate the efficientapplicability of the approach.

Details zur Publikation

Release year: 2008
Language in which the publication is written: English