# The effect of reduced integration in the Steklov eigenvalue problem

- Volume: 38, Issue: 1, page 27-36
- ISSN: 0764-583X

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topArmentano, Maria G.. "The effect of reduced integration in the Steklov eigenvalue problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.1 (2004): 27-36. <http://eudml.org/doc/244681>.

@article{Armentano2004,

abstract = {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.},

author = {Armentano, Maria G.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {finite elements; Steklov eigenvalue problem; reduced integration; finite element; eigenfunctions; eigenvalues; error estimates},

language = {eng},

number = {1},

pages = {27-36},

publisher = {EDP-Sciences},

title = {The effect of reduced integration in the Steklov eigenvalue problem},

url = {http://eudml.org/doc/244681},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Armentano, Maria G.

TI - The effect of reduced integration in the Steklov eigenvalue problem

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 1

SP - 27

EP - 36

AB - 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.

LA - eng

KW - finite elements; Steklov eigenvalue problem; reduced integration; finite element; eigenfunctions; eigenvalues; error estimates

UR - http://eudml.org/doc/244681

ER -

## References

top- [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. Zbl1041.65086
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- [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. Zbl0998.76046
- [6] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). Zbl0804.65101MR1278258
- [7] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). Zbl0383.65058MR520174
- [8] P. Grisvard, Elliptic Problems in Nonsmooth Domain. Pitman Boston (1985). Zbl0695.35060MR775683
- [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). Zbl0296.49033MR400004

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