Jérôme Droniou, Thierry Gallouët (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We prove the convergence of a finite volume method for a noncoercive linear elliptic problem, with right-hand side in the dual space of the natural energy space of the problem.
John W. Barrett, James F. Blowey (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Éric Boillat (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the...
A. Agouzal, M. El Alami El Ferricha (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, a conforming mixed finite element method which takes into account an approximation of the middle line of the arch is given. But for a very small thickness such a method gives poor error bounds. the conforming Galerkin method is then enriched with residual-free bubble functions.
Handlovičová, Angela (1996)
Acta Mathematica Universitatis Comenianae. New Series
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Annalisa Buffa, Yvon Maday, Francesca Rapetti (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements...
Stanislav Sysala (2010)
Applications of Mathematics
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A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence...
Serge Blancher, René Creff, Gérard Gagneux, Bruno Lacabanne, François Montel, David Trujillo (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Our aim here is to study the thermal diffusion phenomenon in a forced convective flow. A system of nonlinear parabolic equations governs the evolution of the mass fractions in multicomponent mixtures. Some existence and uniqueness results are given under suitable conditions on state functions. Then, we present a numerical scheme based on a “mixed finite element” method adapted to a finite volume scheme, of which we give numerical analysis. In a last part, we apply an homogenization technique...