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Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation.
- Source :
-
Calcolo . Sep2009, Vol. 46 Issue 3, p157-185. 29p. - Publication 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUATIONS
*ERROR analysis in mathematics
*NUMERICAL analysis
*MATHEMATICS
*ERRORS
Subjects
Details
- Language :
- English
- ISSN :
- 00080624
- Volume :
- 46
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Calcolo
- Publication Type :
- Academic Journal
- Accession number :
- 52539563
- Full Text :
- https://doi.org/10.1007/s10092-009-0005-x