The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
@article{M2AN_2010__44_3_401_0,
author = {Hetmaniuk, Ulrich L. and Lehoucq, Richard B.},
title = {A special finite element method based on component mode synthesis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {44},
year = {2010},
pages = {401-420},
doi = {10.1051/m2an/2010007},
mrnumber = {2666649},
zbl = {1190.65173},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2010__44_3_401_0}
}
Hetmaniuk, Ulrich L.; Lehoucq, Richard B. A special finite element method based on component mode synthesis. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) pp. 401-420. doi : 10.1051/m2an/2010007. http://gdmltest.u-ga.fr/item/M2AN_2010__44_3_401_0/
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