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The effect of reduced integrationin the Steklov eigenvalue problem

Published online by Cambridge University Press:  15 February 2004

María G. Armentano
María G. Armentano*
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina. [email protected].
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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.

Keywords

Finite elementsSteklov eigenvalueproblemreduced integration.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 1 , January 2004 , pp. 27 - 36
Copyright
© EDP Sciences, SMAI, 2004

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References

Armentano, M.G. and Durán, R.G., Mass lumping or not mass lumping for eigenvalue problems. Numer. Methods Partial Differential Equations 19 (2003) 653–664. CrossRef
I. Babuska and J. Osborn, Eigenvalue Problems, Handbook of Numerical Analysis, Vol. II. Finite Element Methods (Part. 1) (1991).
Banerjee, U. and Osborn, J., Estimation of the effect of numerical integration in finite element eigenvalue approximation. Numer. Math. 56 (1990) 735–762. CrossRef
Belgacem, F.B. and Brenner, S.C., Some nonstandard finite element estimates with applications to 3D Poisson and Signorini problems. Electron. Trans. Numer. Anal. 12 (2001) 134–148.
Bermudez, A., Rodriguez, R. and Santamarina, D., A finite element solution of an added mass formulation for coupled fluid-solid vibrations. Numer. Math. 87 (2000) 201–227. CrossRef
S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994).
P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
P. Grisvard, Elliptic Problems in Nonsmooth Domain. Pitman Boston (1985).
H.J.-P. Morand and R. Ohayon, Interactions Fluids-Structures. Rech. Math. Appl. 23 (1985).
H.F. Weinberger, Variational Methods for Eigenvalue Approximation. SIAM, Philadelphia (1974).