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In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
@article{M2AN_2004__38_1_27_0,
author = {Armentano, Maria G.},
title = {The effect of reduced integration in the {Steklov} eigenvalue problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {27--36},
publisher = {EDP-Sciences},
volume = {38},
number = {1},
year = {2004},
doi = {10.1051/m2an:2004002},
mrnumber = {2073929},
zbl = {1077.65115},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004002/}
}
TY - JOUR AU - Armentano, Maria G. TI - The effect of reduced integration in the Steklov eigenvalue problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 27 EP - 36 VL - 38 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004002/ DO - 10.1051/m2an:2004002 LA - en ID - M2AN_2004__38_1_27_0 ER -
%0 Journal Article %A Armentano, Maria G. %T The effect of reduced integration in the Steklov eigenvalue problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2004 %P 27-36 %V 38 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004002/ %R 10.1051/m2an:2004002 %G en %F M2AN_2004__38_1_27_0
Armentano, Maria G. The effect of reduced integration in the Steklov eigenvalue problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 1, pp. 27-36. doi: 10.1051/m2an:2004002
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