Two-scale FEM for homogenization problems

Ana-Maria Matache; Christoph Schwab

Displaying similar documents to “Two-scale FEM for homogenization problems”

Discrete Sobolev inequalities and $L^{p}$ error estimates for finite volume solutions of convection diffusion equations

Yves Coudière, Thierry Gallouët, Raphaèle Herbin (2001)

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

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The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce $L^{p}$ error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.

Convergence of a Finite Difference Method for the Third BVP for Poisson's Equation

Boško Jovanović, Branislav Popović (1999)

Matematički Vesnik

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On homogenization of elliptic equations with random coefficients.

Conlon, Joseph G., Naddaf, Ali (2000)

Electronic Journal of Probability [electronic only]

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Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching...

Multicomponent flow in a porous medium. Adsorption and Soret effect phenomena : local study and upscaling process

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...

Homogenization and diffusion asymptotics of the linear Boltzmann equation

Thierry Goudon, Antoine Mellet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

Relaxation of quasilinear elliptic systems via A-quasiconvex envelopes

Uldis Raitums (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the weak closure $W Z$ of the set $Z$ of all feasible pairs (solution, flow) of the family of potential elliptic systems where $Ω \subset 𝐑^{n}$ is a bounded Lipschitz domain, $F_{s}$ are strictly convex smooth functions with quadratic growth and $S = {σ m e a s u r a b l e ∣ σ_{s} (x) = 0 or 1, s = 1, \dots, s_{0}, σ_{1} (x) + \dots + σ_{s_{0}} (x) = 1}$ . We show that $W Z$ is the zero level set for an integral functional with the integrand $Q ℱ$ being the $𝐀$ -quasiconvex envelope for a certain function $ℱ$ and the operator $𝐀 = {(curl,div)}^{m}$ . If the functions $F_{s}$ are isotropic, then on the characteristic cone...

The boundary behavior of a composite material

Maria Neuss-Radu (2001)

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

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In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order $ε$ in the energy norm.