Majoration du nombre de résonances près de l'axe réel (d'après un travail avec M. Zworski)
Majoration en norme hölderienne de la résolvante du laplacien dans un ouvert avec coins
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...
Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem.
Mathematical modeling of time-harmonic aeroacoustics with a generalized impedance boundary condition
We study the time-harmonic acoustic scattering in a duct in presence of a flow and of a discontinuous impedance boundary condition. Unlike a continuous impedance, a discontinuous one leads to still open modeling questions, as in particular the singularity of the solution at the abrupt transition and the choice of the right unknown to formulate the scattering problem. To address these questions we propose a mathematical approach based on variational formulations set in weighted Sobolev spaces. Considering...
Mean value theorems for linear and semi-linear rotation invariant operators
Meilleures estimations asymptotiques des restes de la fonction spectrale et des valeurs propres relatifs au laplacien
Meillieurs estimations asymptotiques des restes de la fonctionn spectrale et des valeurs propres relatifs au laplacien.
Mémoire sur l'intégration des équations aux différences partielles de la Physique mathématique.
Mesures limites pour l’équation de Helmholtz dans le cas non captif
Cet article est consacré à l’étude des mesures limites associées à la solution de l’équation de Helmholtz avec un terme source se concentrant en un point. Le potentiel est supposé et l’opérateur non-captif. La solution de l’équation de Schrödinger semi-classique s’écrit alors micro-localement comme somme finie de distributions lagrangiennes. Sous une hypothèse géométrique, qui généralise l’hypothèse du viriel, on en déduit que la mesure limite existe et qu’elle vérifie des propriétés standard....
Method of interior boundaries in a mixed problem of acoustic scattering.
Méthode de calcul du coefficient de singularité pour la solution du problème de Laplace dans un domaine diédral
Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case
We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case
We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients
This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy...
Moving heat source reconstruction from the Cauchy boundary data.
Multigrid for the Wilson mortar element method.