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Martin Costabel

  1. Potential maps and Hardy spaces on special Lipschitz domains.

    Пт, 06/04/2010 - 15:01 — SomNambul
    Authors: Martin Costabel, Alan McIntosh, Robert J. Taggart
    Subjects: Analysis of PDEs
    Abstract

    Suppose that $\Omega$ is the open region in $\mathbb{R}^n$ above a Lipschitz
    graph and let $d$ denote the exterior derivative on $\mathbb{R}^n$. We
    construct a convolution operator $T$ which preserves support in
    $\overline{\Omega}$, is smoothing of order 1 on the homogeneous function
    spaces, and is a potential map in the sense that $dT$ is the identity on spaces
    of exact forms with support in $\overline{\Omega}$.

  2. Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra.

    Ср, 02/10/2010 - 16:01 — SomNambul
    Authors: Martin Costabel, Monique Dauge, Serge Nicaise
    Subjects: Analysis of PDEs
    Abstract

    We prove weighted anisotropic analytic estimates for solutions of model
    elliptic boundary value problems in polyhedra. The weighted analytic classes
    which we use are the same as those introduced by B. Guo in 1993 in view of
    establishing exponential convergence for hp methods in polyhedra. We first give
    a simple proof of the weighted analytic regularity in a polygon, relying on new
    elliptic a priori estimates with analytic control of derivatives in smooth
    domains. The technique is based on dyadic partitions near the corners.

  3. Shape derivatives of boundary integral operators in electromagnetic scatterings.

    Втр, 02/09/2010 - 16:01 — SomNambul
    Authors: Martin Costabel, Frédérique Le Louër
    Subjects: Numerical Analysis
    Abstract

    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 equations are a classical tool to solve
    electromagnetic scattering problems, we study the shape differentiability
    properties of the standard electromagnetic boundary integral operators.

  4. On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body.

    Ср, 12/09/2009 - 16:01 — SomNambul
    Authors: Martin Costabel, Frédérique Le Louër
    Subjects: Numerical Analysis
    Abstract

    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 the electric and magnetic current
    densities on the interface ?. In this paper, following an idea developped by R.
    Kleinman and P. Martin [18] for acoustic scattering problems, we consider
    methods for solving the dielectric scattering problem using a single integral
    equation over ? for a single unknown density.

  5. Discrete compactness for the p-version of discrete differential forms.

    Втр, 09/29/2009 - 15:21 — SomNambul
    Authors: Daniele Boffi, Martin Costabel, Monique Dauge, Leszek Demkowicz, Ralf Hiptmair
    Subjects: Numerical Analysis
    Abstract

    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 three space dimensions. In a very general framework, we
    find sufficient conditions for the p-version of a generalized discrete
    compactness property, which is formulated in the setting of discrete
    differential forms of any order on a d-dimensional polyhedral domain. One of
    the main tools for the analysis is a recently introduced smoothed Poincar\'e
    lifting operator [M. Costabel and A.

  6. Discrete compactness for the p-version of discrete differential forms.

    Втр, 09/29/2009 - 15:21 — SomNambul
    Authors: Daniele Boffi, Martin Costabel, Monique Dauge, Leszek Demkowicz, Ralf Hiptmair
    Subjects: Numerical Analysis
    Abstract

    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 three space dimensions. In a very general framework, we
    find sufficient conditions for the p-version of a generalized discrete
    compactness property, which is formulated in the setting of discrete
    differential forms of any order on a d-dimensional polyhedral domain. One of
    the main tools for the analysis is a recently introduced smoothed Poincar\'e
    lifting operator [M. Costabel and A.

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