Displaying similar documents to “Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition”

On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation

Georgios E. Zouraris (2001)

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

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We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the L 2 norm. We prove optimal order a priori error estimates in the L 2 and H 1 norms, under mild mesh conditions for two and three space dimensions.

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.

On fully practical finite element approximations of degenerate Cahn-Hilliard systems

John W. Barrett, James F. Blowey, Harald Garcke (2001)

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

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We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments...

Finite volume schemes for the p-laplacian on cartesian meshes

Boris Andreianov, Franck Boyer, Florence Hubert (2004)

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

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This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible,...

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...

A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines

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...