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.

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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {46}, number = {6}, year = {2012}, pages = {1555-1576}, doi = {10.1051/m2an/2012016}, zbl = {1276.65069}, mrnumber = {2996340}, language = {en}, url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, pp. 1555-1576. doi : 10.1051/m2an/2012016. http://www.numdam.org/item/M2AN_2012__46_6_1555_0/

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