Lyapunov-Based Error Bounds for the Reduced-Basis Method | Zendy

Robert O’Connor | Zendy

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Lyapunov-Based Error Bounds for the Reduced-Basis Method

Author(s) -

Robert O’Connor

Publication year - 2016

Publication title -

ifac-papersonline

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.308

H-Index - 72

eISSN - 2405-8971

pISSN - 2405-8963

DOI - 10.1016/j.ifacol.2016.07.409

Subject(s) - time stepping , basis (linear algebra) , space (punctuation) , computer science , stability (learning theory) , lyapunov function , mathematics , dynamics (music) , lyapunov stability , pessimism , mathematical optimization , control theory (sociology) , mathematical analysis , control (management) , geometry , artificial intelligence , physics , nonlinear system , quantum mechanics , machine learning , discretization , acoustics , operating system , philosophy , epistemology

We introduce two new error bounds for the reduced-basis method. Existing error bounds for parabolic problems can be classified as either space time or time stepping. Space-time bounds are much more costly and often become unpractical. The cheaper times-stepping bounds have always failed to adequately represent the dynamics of systems containing noncoercive operators. As a result they have always produced extremely pessimistic bounds. Our new bounds are time-stepping bounds that make use of the Lyapunov stability theory to better capture the dynamics of the system.

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