Geodesic
Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems
Fumagalli, Ivan1 ; Manzoni, Andrea2  ; Parolini, Nicola1 ; Verani, Marco1 
1 MOX – Modellistica e Calcolo Scientifico, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy.
2 CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1857-1885

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We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the parameters, the error between the high-fidelity finite element approximation of the first eigenpair and the corresponding reduced basis approximation. The proposed error estimators are exploited not only to certify the RB approximation with respect to the high-fidelity one, but also to set up a greedy algorithm for the offline construction of a reduced basis space. Several numerical experiments show the overall validity of the proposed RB approach.

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Accepté le :
DOI : 10.1051/m2an/2016009
Classification : 65M15, 65N25, 65N30, 78M34
Keywords: Parametrized eigenvalue problems, reduced basis method, a posteriori error estimation, greedy algorithm, dual weighted residual

Fumagalli, Ivan 1 ; Manzoni, Andrea 2 ; Parolini, Nicola 1 ; Verani, Marco 1

1 MOX – Modellistica e Calcolo Scientifico, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy.
2 CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland. 
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     title = {Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1857--1885},
     publisher = {EDP-Sciences},
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Fumagalli, Ivan; Manzoni, Andrea; Parolini, Nicola; Verani, Marco. Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1857-1885. doi: 10.1051/m2an/2016009

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