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The main goal of this article is to establish a priori and a posteriori
error estimates for the numerical approximation of some non linear elliptic
problems arising in glaciology. The stationary motion of a glacier is given
by a non-Newtonian fluid flow model which becomes, in a first
two-dimensional approximation, the so-called infinite parallel sided slab
model. The approximation of this model is made by a finite element method
with piecewise polynomial functions of degree 1. Numerical results...
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally,...
In this paper, we concern ourselves with uniqueness results for an elliptic-parabolic quasilinear partial differential equation describing, for instance, the pressure of a fluid in a three-dimensional porous medium: within the frame of mathematical modeling of the secondary recovery from oil fields, the handling of the component conservation laws leads to a system including such a pressure equation, locally elliptic or parabolic according to the evolution of the gas phase.
We propose a new formulation of the 3D Boltzmann
non linear operator, without assuming Grad's angular cutoff
hypothesis, and
for intermolecular laws behaving as 1/rs, with s> 2. It involves
natural pseudo differential operators, under a form which is analogous
to the Landau operator. It may be used in the study of the
associated equations, and more precisely in the non homogeneous
framework.
Cet article propose d’aborder la question de l’écriture des textes scientifiques en partant d’une méthodologie comparative. En choisissant deux textes assez proches du même auteur sur le même sujet (en l’occurrence des travaux de Navier sur l’écoulement des fluides dans les années 1820), on peut mettre en évidence des variations dans les formulations et dans la composition des textes. Ces différences peuvent parfois être attribuées aux genres des périodiques dans lesquels ils ont paru. Mais surtout,...
This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time
dependent case. Whereas in the second part some preliminary numerical simulations aim to
give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the first part, the time dependent rough problem for a simplified heat
equation in a straight channel that mimics the axial...
The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale,
so that we can asymptotically reduce them to immersed polygonal fault
interfaces and the model finally consists in a coupling between...
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