On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Toni Lassila; Andrea Manzoni; Gianluigi Rozza

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1555-1576
  • ISSN: 0764-583X

Abstract

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A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this bound is extended to the fine level by adding a proper correction term. Because the approximate problems are affine, an efficient offline/online computational scheme can be developed for the certified solution (error bounds and stability factors) of the parametric equations considered. We experiment with different correction terms suited for a posteriori error estimation of the reduced basis solution of elliptic coercive and noncoercive problems.

How to cite

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Lassila, Toni, Manzoni, Andrea, and Rozza, Gianluigi. "On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1555-1576. <http://eudml.org/doc/277839>.

@article{Lassila2012,
abstract = {A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this bound is extended to the fine level by adding a proper correction term. Because the approximate problems are affine, an efficient offline/online computational scheme can be developed for the certified solution (error bounds and stability factors) of the parametric equations considered. We experiment with different correction terms suited for a posteriori error estimation of the reduced basis solution of elliptic coercive and noncoercive problems.},
author = {Lassila, Toni, Manzoni, Andrea, Rozza, Gianluigi},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Parametric model reduction; a posteriori error estimation; stability factors; coercivity constant; inf-sup condition; parametrized PDEs; reduced basis method; successive constraint method; empirical interpolation; parametric model reduction; a posteriori error estimation; algorithm; Poisson problem},
language = {eng},
month = {8},
number = {6},
pages = {1555-1576},
publisher = {EDP Sciences},
title = {On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition},
url = {http://eudml.org/doc/277839},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Lassila, Toni
AU - Manzoni, Andrea
AU - Rozza, Gianluigi
TI - On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/8//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1555
EP - 1576
AB - A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this bound is extended to the fine level by adding a proper correction term. Because the approximate problems are affine, an efficient offline/online computational scheme can be developed for the certified solution (error bounds and stability factors) of the parametric equations considered. We experiment with different correction terms suited for a posteriori error estimation of the reduced basis solution of elliptic coercive and noncoercive problems.
LA - eng
KW - Parametric model reduction; a posteriori error estimation; stability factors; coercivity constant; inf-sup condition; parametrized PDEs; reduced basis method; successive constraint method; empirical interpolation; parametric model reduction; a posteriori error estimation; algorithm; Poisson problem
UR - http://eudml.org/doc/277839
ER -

References

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