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The aim of this paper is to develop a finite element method which allows computing
the buckling coefficients and modes of a non-homogeneous Timoshenko beam.
Studying the spectral properties of a non-compact operator,
we show that the relevant buckling coefficients correspond to isolated
eigenvalues of finite multiplicity.
Optimal order error estimates are proved for the eigenfunctions
as well as a double order of convergence for
the eigenvalues using classical abstract spectral approximation theory...
The aim of this paper is to develop a finite element method which allows computing
the buckling coefficients and modes of a non-homogeneous Timoshenko beam.
Studying the spectral properties of a non-compact operator,
we show that the relevant buckling coefficients correspond to isolated
eigenvalues of finite multiplicity.
Optimal order error estimates are proved for the eigenfunctions
as well as a double order of convergence for
the eigenvalues using classical abstract spectral approximation theory...
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci. 342 (2006) 883–886; CALCOLO 45 (2008) 111–147; J. Sci. Comput. 38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions to obtain fast convergence of domain decomposition...
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci.342 (2006) 883–886; CALCOLO45 (2008) 111–147; J. Sci. Comput.38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions
to obtain fast convergence of domain decomposition...
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned...
We present in this article two components: these components can in fact serve various goals
independently, though we consider them here as an ensemble. The first component is a technique for
the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and
parabolic) partial differential equations with affine parameter dependence.
The essential features are (i) (provably) rapidly convergent global
reduced–basis approximations — Galerkin projection onto a space
WN spanned...
A Mimetic Discretization method for the linear elasticity problem
in mixed weakly symmetric form is developed. The scheme is shown to
converge linearly in the mesh size, independently of the
incompressibility parameter λ, provided the discrete scalar
product satisfies two given conditions. Finally, a family of
algebraic scalar products which respect the above conditions is
detailed.
A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...
We introduce and analyse a mixed formulation of the
Monge-Kantorovich equations, which express optimality conditions for
the mass transportation problem with cost proportional to distance.
Furthermore, we introduce and analyse the finite element
approximation of this formulation using the lowest order
Raviart-Thomas element. Finally, we present some numerical
experiments, where both the optimal transport density and the
associated Kantorovich potential are computed for a coupling problem
and problems...
We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.
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375