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A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, n , in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type [ γ , + [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2001)

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

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators A n , n , in a suitable Hilbert space. We show that the essential spectrum of A n is an interval of type [ γ , + [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

About asymptotic approximations in thin waveguides

Nicole Turbe, Louis Ratier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the propagation of electromagnetic waves in a guide the section of which is a thin annulus. Owing to the presence of a small parameter, explicit approximations of the TM and TE eigenmodes are obtained. The cases of smooth and non smooth boundaries are presented.

About asymptotic approximations in thin waveguides

Nicole Turbe, Louis Ratier (2005)

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

We study the propagation of electromagnetic waves in a guide the section of which is a thin annulus. Owing to the presence of a small parameter, explicit approximations of the TM and TE eigenmodes are obtained. The cases of smooth and non smooth boundaries are presented.

Bloch wave homogenization of linear elasticity system

Sista Sivaji Ganesh, Muthusamy Vanninathan (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...

Bloch wave homogenization of linear elasticity system

Sista Sivaji Ganesh, Muthusamy Vanninathan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...

Error estimates for the ultra weak variational formulation in linear elasticity

Teemu Luostari, Tomi Huttunen, Peter Monk (2013)

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

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2(Ω) norm in terms of the best approximation...

Error estimates for the ultra weak variational formulation in linear elasticity∗

Teemu Luostari, Tomi Huttunen, Peter Monk (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate...

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