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Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation

Content Provider	Springer Nature Link
Author	Nguyen, Ngoc Cuong Patera, Anthony T. Rozza, Gianluigi
Copyright Year	2009
Abstract	In this paper we present rigorous a posteriori L 2 error bounds for reduced basis approximations of the unsteady viscous Burgers’ equation in one space dimension. The a posteriori error estimator, derived from standard analysis of the error-residual equation, comprises two key ingredients—both of which admit efficient Offline-Online treatment: the first is a sum over timesteps of the square of the dual norm of the residual; the second is an accurate upper bound (computed by the Successive Constraint Method) for the exponential-in-time stability factor. These error bounds serve both Offline for construction of the reduced basis space by a new POD-Greedy procedure and Online for verification of fidelity. The a posteriori error bounds are practicable for final times (measured in convective units) T≈O(1) and Reynolds numbers ν −1≫1; we present numerical results for a (stationary) steepening front for T=2 and 1≤ν −1≤200.
Ending Page	185
Page Count	29
Starting Page	157
File Format	PDF
ISSN	00080624
e-ISSN	11265434
Journal	CALCOLO
Issue Number	3
Volume Number	46
Language	English
Publisher	Springer Milan
Publisher Date	2009-06-30
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stability and convergence of numerical methods Proper orthogonal decomposition Reduced basis A posteriori error bounds Greedy sampling Numerical Analysis Burgers’ equation Error bounds Stability factor Theory of Computation Successive constraint method
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Mathematics

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