74 citations · 409 across the 32 of their papers we have counts for
14 papers · 1 filter
Stability Analysis of a Simple Discretization Method for a Class of Strongly Singular Integral Equations
Martin Costabel, Monique Dauge, Khadijeh Nedaiasl
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lip…
Corner asymptotics of the magnetic potential in the eddy-current model
Monique Dauge, Patrick Dular, Laurent Krähenbühl +3
In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the…
High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero
Marie Chaussade-Beaudouin, Monique Dauge, Erwan Faou +1
The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2) tends to zero. Using a novel asymp…
Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases
Marie Chaussade-Beaudouin, Monique Dauge, Erwan Faou +1
Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{é} system) are determined by an asymptotic analysis as the…
Continuity properties of the inf-sup constant for the divergence
Christine Bernardi, Martin Costabel, Monique Dauge +1
The inf-sup constant for the divergence, or LBB constant, is explicitly known for only few domains. For other domains, upper and lower estimates are known. If more precise values a…
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
Monique Dauge, Thomas Ourmières-Bonafos, Nicolas Raymond
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture l…
The inf-sup constant for the divergence on corner domains
Martin Costabel, Michel Crouzeix, Monique Dauge +1
The inf-sup constant for the divergence, or LBB constant, is related to the Cosserat spectrum. It has been known for a long time that on non-smooth domains the Cosserat operator ha…
Regularity for Maxwell eigenproblems in photonic crystal fibre modelling
Monique Dauge, Richard A. Norton, Robert Scheichl
The convergence behaviour and the design of numerical methods for modelling the flow of light in photonic crystal fibres depend critically on an understanding of the regularity of…
On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
Martin Costabel, Monique Dauge
The equivalence between the inequalities of Babuška-Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We pro…
Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90 degree V-notch with Neumann boundary conditions
Samuel Shannon, Zohar Yosibash, Monique Dauge +1
This report presents explicit analytical expressions for the primal, primal shadows, dual and dual shadows functions for the Laplace equation in the vicinity of a circular singular…
Quantum waveguides with corners
Monique Dauge, Yvon Lafranche, Nicolas Raymond
The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we…
Non-coercive transmission problems in polygonal domains. -- Problèmes de transmission non coercifs dans des polygones
Monique Dauge, Benjamin Texier
We show that Kondratev's theory for corner domains can be extended to scalar transmission problems between two polygonal materials if the contrast ratio between the two materials i…
Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism
Gabriel Caloz, Monique Dauge, Victor Péron
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio betwee…
Discrete compactness for the p-version of discrete differential forms
Daniele Boffi, Martin Costabel, Monique Dauge +2
In this paper we prove the discrete compactness property for a wide class of p-version finite element approximations of non-elliptic variational eigenvalue problems in two and thre…