Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation
Name
Patera_Reduced basis approximation.pdf
Size
470.22 KB
Format
Adobe PDF
Checksum (MD5)
10069e0e120f70931cbb584e06bc5715
Author(s)
Nguyen, Ngoc Cuong
Rozza, Gianluigi
Patera, Anthony T.
Date Issued
June 2009
Journal
Calcolo
Publisher
Springer-Verlag
Citation
Nguyen, Ngoc-Cuong, Gianluigi Rozza, and Anthony T. Patera. Reduced Basis Approximation and a Posteriori Error Estimation for the Time-dependent Viscous Burgers’ Equation. Calcolo 46, no. 3 (September 30, 2009): 157-185.
Version
Author's final manuscript
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[superscript −1]≫1; we present numerical results for a (stationary) steepening front for T=2 and 1≤ν[superscript −1]≤200.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10092-009-0005-x
