# 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

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topLassila, 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 -

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