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Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Nguyen, Ngoc Cuong Rozza, Gianluigi Patera, Anthony T. |
| Copyright Year | 2009 |
| Abstract | In this paper we present rigorous a posterioriL2 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. |
| Starting Page | 157 |
| Ending Page | 185 |
| Page Count | 29 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10092-009-0005-x |
| Volume Number | 46 |
| Alternate Webpage(s) | http://dspace.mit.edu/openaccess-disseminate/1721.1/81221 |
| Alternate Webpage(s) | https://infoscience.epfl.ch/record/125130/files/ATP_Burgers_Calcolo_sp.pdf |
| Alternate Webpage(s) | http://dspace.mit.edu/bitstream/handle/1721.1/81221/Patera_Reduced%20basis%20approximation.pdf;sequence=1 |
| Alternate Webpage(s) | http://augustine.mit.edu/methodology/papers/atpCalcoloApr2009preprint.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10092-009-0005-x |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
