5 research outputs found
On Error Estimation for Reduced-order Modeling of Linear Non-parametric and Parametric Systems
Motivated by a recently proposed error estimator for the transfer function of
the reduced-order model of a given linear dynamical system, we further develop
more theoretical results in this work. Furthermore, we propose several variants
of the error estimator, and compare those variants with the existing ones both
theoretically and numerically. It has been shown that some of the proposed
error estimators perform better than or equally well as the existing ones. All
the error estimators considered can be easily extended to estimate output error
of reduced-order modeling for steady linear parametric systems.Comment: 34 pages, 12 figure
(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
We consider ultraweak variational formulations for (parametrized) linear
first order transport equations in time and/or space. Computationally feasible
pairs of optimally stable trial and test spaces are presented, starting with a
suitable test space and defining an optimal trial space by the application of
the adjoint operator. As a result, the inf-sup constant is one in the
continuous as well as in the discrete case and the computational realization is
therefore easy. In particular, regarding the latter, we avoid a stabilization
loop within the greedy algorithm when constructing reduced models within the
framework of reduced basis methods. Several numerical experiments demonstrate
the good performance of the new method