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On the approximation of stability factors for generalparametrized partial differential equations with a two-level affinedecomposition

Published online by Cambridge University Press:  01 August 2012

Toni Lassila ,
Andrea Manzoni  and
Gianluigi Rozza
Toni Lassila
Affiliation:
Modelling and Scientific Computing, Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland. [email protected]; [email protected]; [email protected]
Andrea Manzoni
Affiliation:
Modelling and Scientific Computing, Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland. [email protected]; [email protected]; [email protected]
Gianluigi Rozza
Affiliation:
Modelling and Scientific Computing, Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland. [email protected]; [email protected]; [email protected]
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Abstract

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.

Keywords

Parametric model reductiona posteriori error estimationstability factorscoercivity constantinf-sup conditionparametrized PDEsreduced basis methodsuccessive constraint methodempirical interpolation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1555 - 1576
Copyright
© EDP Sciences, SMAI, 2012

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