Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 50, Issue 1, Pages 46-63Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110822724
Keywords
nonlinear model reduction; proper orthogonal decomposition; empirical interpolation methods; nonlinear partial differential equations
Categories
Funding
- NSF [CCF-1017401]
- AFOSR [FA9550-09-1-0225]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1017401] Funding Source: National Science Foundation
Ask authors/readers for more resources
This paper derives state space error bounds for the solutions of reduced systems constructed using proper orthogonal decomposition (POD) together with the discrete empirical interpolation method (DEIM) recently developed for nonlinear dynamical systems [SIAM J. Sci. Comput., 32 (2010), pp. 2737-2764]. The resulting error estimates are shown to be proportional to the sums of the singular values corresponding to neglected POD basis vectors both in Galerkin projection of the reduced system and in the DEIM approximation of the nonlinear term. The analysis is particularly relevant to ODE systems arising from spatial discretizations of parabolic PDEs. The derivation clearly identifies where the parabolicity is crucial. It also explains how the DEIM approximation error involving the nonlinear term comes into play.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available