A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems
Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011) held in Paris, France, 6-8 June 2011,, page 365--376, - may 2011
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We extend previous work on the Hierarchical Model Reduction-Reduced
Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to
the Boussinesq approach we do not neglect the dependency on the vertical direction but
enhance the solution for the horizontal direction with appropriately chosen basis functions
living on the vertical one. This is done by a combination of the frameworks of hierarchical
model reduction and the reduced basis methods. We derive a new a posteriori error
estimate and demonstrate in numerical experiments that few basis functions suffice to get
good approximations.
BibTex references
@InProceedings{OS11,
author = {Ohlberger, M. and Smetana, K.},
title = {A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems},
booktitle = {Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011) held in Paris, France, 6-8 June 2011,},
pages = {365--376,},
month = {may},
year = {2011},
editor = {D. Aubry, P. D\íez, B. Tie, N. Par\és (Eds.)},
publisher = {International Center for Numerical Methods in Engineering (CIMNE), Barcelona,},
keywords = {model reduction},
url = \{/2011/OS11},
}
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