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On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations

Eliane Bécache, Patrick Joly (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This...

On the approximation of front propagation problems with nonlocal terms

Pierre Cardaliaguet, Denis Pasquignon (2001)

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

We investigate the approximation of the evolution of compact hypersurfaces of ℝ N depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.

On the approximation of front propagation problems with nonlocal terms

Pierre Cardaliaguet, Denis Pasquignon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate the approximation of the evolution of compact hypersurfaces of ℝ N depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.

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

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.

On the double critical-state model for type-II superconductivity in 3D

Yohei Kashima (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...

On the growth of the resolvent operators for power bounded operators

Olavi Nevanlinna (1997)

Banach Center Publications

Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of T n ( T - 1 ) . For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of T n ( T - 1 ) is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating the...

Currently displaying 341 – 360 of 508