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.

Accepted:

DOI: 10.1051/m2an/2016009

Keywords: Parametrized eigenvalue problems, reduced basis method, a posteriori error estimation, greedy algorithm, dual weighted residual

^{1}; Manzoni, Andrea

^{2}; Parolini, Nicola

^{1}; Verani, Marco

^{1}

@article{M2AN_2016__50_6_1857_0, author = {Fumagalli, Ivan and Manzoni, Andrea and Parolini, Nicola and Verani, Marco}, 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}, volume = {50}, number = {6}, year = {2016}, doi = {10.1051/m2an/2016009}, zbl = {1355.65149}, mrnumber = {3580125}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016009/} }

TY - JOUR AU - Fumagalli, Ivan AU - Manzoni, Andrea AU - Parolini, Nicola AU - Verani, Marco TI - Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1857 EP - 1885 VL - 50 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016009/ DO - 10.1051/m2an/2016009 LA - en ID - M2AN_2016__50_6_1857_0 ER -

%0 Journal Article %A Fumagalli, Ivan %A Manzoni, Andrea %A Parolini, Nicola %A Verani, Marco %T Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1857-1885 %V 50 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016009/ %R 10.1051/m2an/2016009 %G en %F M2AN_2016__50_6_1857_0

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