129 citations · 369 across the 23 of their papers we have counts for
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Convergence of a simple discretization of the finite Hilbert transformation
Martin Costabel
For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, b…
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…
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…
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…
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…
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
Martin Costabel, Frédérique Le Louër
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral…
Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators
Martin Costabel, Frédérique Le Louër
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting bet…
Shape derivatives of boundary integral operators in electromagnetic scattering
Martin Costabel, Frédérique Le Louër
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral…
On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body
Martin Costabel, Frédérique Le Louër
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for…
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…