An online intrinsic stabilization strategy for the reduced basis approximation of parametrized advection-dominated problems

We propose a new, black-box online stabilization strategy for reduced basis (RB) approximations of parameter-dependent advection-diffusion problems in the advection-dominated case. Our goal is to stabilize the RB problem irrespectively of the stabilization (if any) operated on the high-fidelity (e.g., finite element) approximation, provided a set of stable RB functions have been computed. Inspired by the spectral vanishing viscosity method, our approach relies on the transformation of the basis functions into modal basis, then on the addition of a vanishing viscosity term over the high RB modes, and on a rectification stage - prompted by the spectral filtering technique-to further enhance the accuracy of the RB approximation. Numerical results dealing with an advection-dominated problem parametrized with respect to the diffusion coefficient show the accuracy of the RB solution on the whole parametric range. (C) 2016 Published by Elsevier Masson SAS on behalf of Academie des sciences. This is an open access article under the CC BY-NC-ND license.


Published in:
Comptes Rendus Mathematique, 354, 12, 1188-1194
Year:
2016
Publisher:
Paris, Elsevier France-Editions Scientifiques Medicales Elsevier
ISSN:
1631-073X
Laboratories:




 Record created 2017-01-24, last modified 2018-09-13


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)