Wirtz, D.; Sorensen, D. C.; Haasdonk, B. A posteriori error estimation for DEIM reduced nonlinear dynamical systems. (English) Zbl 1312.65127 SIAM J. Sci. Comput. 36, No. 2, 311-338 (2014). The authors introduce a novel approach for a posteriori error estimation of nonlinear dynamical systems reduced by a subspace projection and the discrete empirical interpolation method (DEIM) approximation of the system’s nonlinearities. The reduction process is based on both applying the Galerkin projection of the full nonlinear system into a suitable linear subspace and applying the DEIM method to approximate the system’s nonlinearity. The computations for a posteriori error estimators are efficiently decomposed in an offline/online fashion. The effectiveness of the proposed approach for a posteriori error estimation is discussed via two numerical examples: a one-dimensional viscous Burger equation and a two-dimensional reaction-diffusion model for cell apoptosis.The reviewer believes that the proposed algorithm is effective and applicable to a wide range class of nonlinear dynamical systems. Reviewer: Qasem Al-Mdallal (Al-Ain) Cited in 37 Documents MSC: 65L70 Error bounds for numerical methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35K57 Reaction-diffusion equations Keywords:model reduction; nonlinear dynamical systems; discrete empirical interpolation method; error estimation; offline/online decomposition; Jacobian approximation; partial similarity transform; subspace projection; Galerkin projection; numerical examples; viscous Burgers equation; reaction-diffusion model PDFBibTeX XMLCite \textit{D. Wirtz} et al., SIAM J. Sci. Comput. 36, No. 2, 311--338 (2014; Zbl 1312.65127) Full Text: DOI Link