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.
Mots clés : finite elements, Steklov eigenvalue problem, reduced integration
@article{M2AN_2004__38_1_27_0, author = {Armentano, Maria G.}, title = {The effect of reduced integration in the {Steklov} eigenvalue problem}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, 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://www.numdam.org/articles/10.1051/m2an:2004002/} }
TY - JOUR AU - Armentano, Maria G. TI - The effect of reduced integration in the Steklov eigenvalue problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 27 EP - 36 VL - 38 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/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: Modélisation mathématique et analyse numérique %D 2004 %P 27-36 %V 38 %N 1 %I EDP-Sciences %U http://www.numdam.org/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: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 1, pp. 27-36. doi : 10.1051/m2an:2004002. http://www.numdam.org/articles/10.1051/m2an:2004002/
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