The effect of reduced integration in the Steklov eigenvalue problem
Armentano, Maria G.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004), p. 27-36 / Harvested from Numdam
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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.

Publié le : 2004-01-01
DOI : https://doi.org/10.1051/m2an:2004002
Classification:  65D30,  65N25,  65N30 
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {38},
     year = {2004},
     pages = {27-36},
     doi = {10.1051/m2an:2004002},
     mrnumber = {2073929},
     zbl = {1077.65115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 27-36. doi : 10.1051/m2an:2004002. http://gdmltest.u-ga.fr/item/M2AN_2004__38_1_27_0/

[1] M.G. Armentano and R.G. Durán, Mass lumping or not mass lumping for eigenvalue problems. Numer. Methods Partial Differential Equations 19 (2003) 653-664. | Zbl 1041.65086

[2] I. Babuska and J. Osborn, Eigenvalue Problems, Handbook of Numerical Analysis, Vol. II. Finite Element Methods (Part. 1) (1991). | MR 1115240 | Zbl 0875.65087

[3] U. Banerjee and J. Osborn, Estimation of the effect of numerical integration in finite element eigenvalue approximation. Numer. Math. 56 (1990) 735-762. | Zbl 0693.65071

[4] F.B. Belgacem and S.C. Brenner, Some nonstandard finite element estimates with applications to 3D Poisson and Signorini problems. Electron. Trans. Numer. Anal. 12 (2001) 134-148. | Zbl 0981.65131

[5] A. Bermudez, R. Rodriguez and D. Santamarina, A finite element solution of an added mass formulation for coupled fluid-solid vibrations. Numer. Math. 87 (2000) 201-227. | Zbl 0998.76046

[6] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). | MR 1278258 | Zbl 0804.65101

[7] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). | MR 520174 | Zbl 0383.65058

[8] P. Grisvard, Elliptic Problems in Nonsmooth Domain. Pitman Boston (1985). | MR 775683 | Zbl 0695.35060

[9] H.J.-P. Morand and R. Ohayon, Interactions Fluids-Structures. Rech. Math. Appl. 23 (1985).

[10] H.F. Weinberger, Variational Methods for Eigenvalue Approximation. SIAM, Philadelphia (1974). | MR 400004 | Zbl 0296.49033