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Reduced Basis Approximation and a Posteriori Error Estimation for the Parametrized Unsteady Boussinesq Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Knezevic, David J. Nguyen, Ngoc Cuong Patera, Anthony T. |
| Copyright Year | 2011 |
| Abstract | In this paper we present reduced basis (RB) approximations and associated rigorous a posteriori error bounds for the parametrized unsteady Boussinesq equations. The essential ingredients are Galerkin projection onto a low-dimensional space associated with a smooth parametric manifold — to provide dimension reduction; an efficient proper orthogonal decomposition–Greedy sampling method for identification of optimal and numerically stable approximations — to yield rapid convergence; accurate (online) calculation of the solution-dependent stability factor by the successive constraint method — to quantify the growth of perturbations/residuals in time; rigorous a posteriori bounds for the errors in the RB approximation and associated outputs — to provide certainty in our predictions; and an offline–online computational decomposition strategy for our RB approximation and associated error bound — to minimize marginal cost and hence achieve high performance in the real-time and many-query contexts. The method is applied to a transient natural convection problem in a two-dimensional "complex" enclosure — a square with a small rectangle cutout — parametrized by Grashof number and orientation with respect to gravity. Numerical results indicate that the RB approximation converges rapidly and that furthermore the (inexpensive) rigorous a posteriori error bounds remain practicable for parameter domains and final times of physical interest. |
| Starting Page | 1415 |
| Ending Page | 1442 |
| Page Count | 28 |
| File Format | PDF HTM / HTML |
| DOI | 10.1142/S0218202511005441 |
| Volume Number | 21 |
| Alternate Webpage(s) | http://dspace.mit.edu/openaccess-disseminate/1721.1/80807 |
| Alternate Webpage(s) | http://augustine.mit.edu/methodology/papers/atp_M3AS_preprint_Sep2010.pdf |
| Alternate Webpage(s) | http://www.dam.brown.edu/AFOSR_MURI_pub/atp_M3AS_preprint_Sep2010+Patera_BoussinesqEquations.pdf |
| Alternate Webpage(s) | http://dspace.mit.edu/bitstream/handle/1721.1/80807/Patera_Reduced%20basis%20app.pdf;sequence=1 |
| Alternate Webpage(s) | https://doi.org/10.1142/S0218202511005441 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
