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A state space error estimate for POD-DEIM nonlinear model reduction. (English) Zbl 1237.93035

Summary: 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 by the authors [SIAM J. Sci. Comput., 32, pp. 2737-2764 (2010; Zbl 1217.65169)]. 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.

MSC:

93B11 System structure simplification
93C10 Nonlinear systems in control theory
93C20 Control/observation systems governed by partial differential equations

Citations:

Zbl 1217.65169

Software:

rbMIT
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