The model order reduction methodology of reduced basis (RB)
techniques offers efficient treatment of parametrized partial differential
equations (P2DEs) by providing both approximate solution procedures and
efficient error estimates.
RB-methods have so far mainly been applied to finite element schemes
for elliptic and parabolic problems. In the current study
we extend the methodology to general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations. The new theoretic contributions are the formulation of a reduced basis approximation scheme for these general evolution problems and
the derivation of rigorous a-posteriori error estimates in various norms. Algorithmically, an offline/online decomposition of the scheme and the error estimators is
realized in case of affine parameter-dependence of the problem.
This is the basis for a rapid online computation in case of multiple simulation requests.
We introduce a new offline basis-generation algorithm based on our
a-posteriori error estimator which combines ideas from existing approaches.
Numerical experiments for an instationary convection-diffusion problem
demonstrate the efficient applicability of the approach.