Geodesic
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1555-1576

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/m2an/2012016
Classification : 35J05, 65N15, 65N30
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 
@article{M2AN_2012__46_6_1555_0,
     author = {Lassila, Toni and Manzoni, Andrea and Rozza, Gianluigi},
     title = {On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1555--1576},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {6},
     year = {2012},
     doi = {10.1051/m2an/2012016},
     mrnumber = {2996340},
     zbl = {1276.65069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012016/}
}
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 
PY  - 2012
SP  - 1555
EP  - 1576
VL  - 46
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012016/
DO  - 10.1051/m2an/2012016
LA  - en
ID  - M2AN_2012__46_6_1555_0
ER  - 
%0 Journal Article
%A Lassila, Toni
%A Manzoni, Andrea
%A Rozza, Gianluigi
%T On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2012
%P 1555-1576
%V 46
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012016/
%R 10.1051/m2an/2012016
%G en
%F M2AN_2012__46_6_1555_0
Lassila, Toni; Manzoni, Andrea; 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 , Tome 46 (2012) no. 6, pp. 1555-1576. doi: 10.1051/m2an/2012016

Cité par Sources :