Volume 46, Number 6, November-December 2012
|Page(s)||1555 - 1576|
|Published online||01 August 2012|
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
Modelling and Scientific Computing, Mathematics Institute of
Computational Science and Engineering, École Polytechnique Fédérale de
Lausanne, Station 8,
firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Revised: 30 March 2012
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.
Mathematics Subject Classification: 35J05 / 65N15 / 65N30
Key words: Parametric model reduction / a posteriori error estimation / stability factors / coercivity constant / inf-sup condition / parametrized PDEs / reduced basis method / successive constraint method / empirical interpolation
© EDP Sciences, SMAI, 2012
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