A new approach for computationally efficient estimation of stability factors forparametric partial differential equations is presented. The general parametric bilinearform of the problem is approximated by two affinely parametrized bilinear forms atdifferent levels of accuracy (after an empirical interpolation procedure). The successiveconstraint method is applied on the coarse level to obtain a lower bound for the stabilityfactors, 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 computationalscheme can be developed for the certified solution (error bounds and stability factors) ofthe parametric equations considered. We experiment with different correction terms suitedfor a posteriori error estimation of the reduced basis solution ofelliptic coercive and noncoercive problems.
