Displaying similar documents to “On an internal approximation of a class of elliptic eigenvalue problems”

The effect of reduced integration in the Steklov eigenvalue problem

Maria G. Armentano (2004)

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

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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.

Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Emmanuel Creusé, Serge Nicaise (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theoretical predictions.

Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients

Pulin Kumar Bhattacharyya, Neela Nataraj (2002)

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

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Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field...