Martin Costabel - Recent Publications

greenball M. Costabel, M. Dalla Riva, M. Dauge, P. Musolino: Converging expansions for Lipschitz self-similar perforations of a plane sector.
Integral Equations Operator Theory 88(3) (2017), 401-449.
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--- HAL: hal-01482187 --- arXiv : 1703.01124 --- SpringerLINK

greenball M. Costabel, M. Dauge: Approximation of the inf-sup constant.
(Poster presented at "Advances in Mathematics of Finite Elements", A conference in honor of the 90th birthday of Prof. Ivo Babuška, ICES, Austin, Texas, 21-22 March 2016)
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greenball C. Bernardi, M. Costabel, M. Dauge, V. Girault: Continuity properties of the inf-sup constant for the divergence.
SIAM J. Math. Anal. 48(2) (2016), 1250-1271.
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--- HAL: hal-01215296 --- arXiv : 1510.03978

greenball M. Costabel: Inequalities of Babuška-Aziz and Friedrichs-Velte for differential forms.
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--- HAL: hal-01181963 --- arXiv:1507.08464

greenball M. Costabel, E, Darrigrand, H. Sakly: Volume integral equations for electromagnetic scattering in two dimensions.
Computers and Mathematics with Applications 70(8) (2015), 2087-2101.
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--- HAL: hal-01145730 --- arXiv:1505.05429 --- DOI : 10.1016/j.camwa.2015.08.026

greenball M. Costabel: On the Spectrum of Volume Integral Operators in Acoustic Scattering.
Chap. 11 of: Integral Methods in Science and Engineering. C. Constanda, A. Kirsch (Eds.), Birkhaeuser 2015
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--- HAL: hal-01098834 --- arXiv:1412.8685

greenball M. Costabel: On the Method of Volume Integral Equations
(Slides from a plenary talk at IMSE 2014, Karlsruhe 21-25 July 2014)
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greenball M. Costabel: Computing the inf-sup constant for the divergence
(Slides from a plenary talk at ICOSAHOM 2014, Salt Lake City 22-27 June 2014)
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greenball M. Costabel, M.Dauge, M. Crouzeix, Y. Lafranche: The inf-sup constant for the divergence on corner domains.
Numer. Methods Partial Differential Equations 31 (2015), no. 2, 439-458.
--- HAL: hal-00947143 --- arXiv:1402.36591

greenball M. Costabel: The inf-sup constant of the divergence.
(Slides from a plenary talk at MAFELAP 2013, Uxbridge 14/06/2013)
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greenball M. Costabel, M.Dauge: On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne. (2013)
Arch. Rational Mech. and Anal. 217 (2015) No 3, 873-898. DOI : 10.1007/s00205-015-0845-2
--- HAL: hal-00804385 --- arXiv:1303.6141 --- SpringerLINK

greenball M. Costabel, F. Le Louër: Shape derivatives of boundary integral operators in electromagnetic scattering. (2012)
Part I: Shape differentiability of pseudo-homogeneous boundary integral operators. --- HAL: hal-00592280 --- arXiv:1105.2474 --- SpringerLINK
Part II: Application to scattering by a homogeneous dielectric obstacle. --- HAL: hal-00592282 --- arXiv:1105.2479 --- SpringerLINK

greenball M. Costabel, E. Darrigrand, H. Sakly: The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body. (2011)
--- HAL: hal-00646229 --- CRAS

greenball M. Costabel: The curious importance of function spaces for the Maxwell equations
(Slides from a plenary talk at WAVES 2011, SFU Vancouver 25-29 July 2011)
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greenball M. Costabel: Lectures on the Cosserat Eigenvalue Problem.
(Slides from lectures at the Summer School and Workshop STOP2011, IST Lisbon 24-29 June 2011)
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greenball Z. Yosibash, S. Shannon, M. Dauge, M. Costabel: Circular edge singularities for the Laplace equation and the elasticity system in 3-D domains. (2010)
--- HAL: hal-00490971

greenball M. Costabel, A. McIntosh, R. J. Taggart: Potential maps and Hardy spaces on special Lipschitz domains. (2010)
--- HAL: hal-00490854 --- arXiv:1006.0562

greenball M. Costabel, M. Dauge, S. Nicaise: Analytic regularity for linear elliptic systems in polygons and polyhedra (2010)
--- HAL: hal-00454133 --- arXiv:1002.1772 --- pdf

greenball M. Costabel, F. Le Louër: Shape derivatives of boundary integral operators in electromagnetic scattering. (2010)
--- HAL: hal-00453948 --- pdf

greenball M. Costabel, M. Dauge, S. Nicaise: Corner Singularities and Analytic Regularity for Linear Elliptic Systems. Part I: Smooth domains. (2010)
--- HAL: hal-00453934 --- pdf (1.7MB)

greenball M. Costabel, F. Le Louër: On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body. (2009)
--- HAL: hal-00439221 --- arXiv:0912.1419 --- pdf --- SIAP 71 (2011) 635-656

greenball D. Boffi, M. Costabel, M. Dauge, L. Demkowicz, R. Hiptmair: Discrete compactness for the p-version of discrete differential forms. (2009)
--- Abstract --- HAL: hal-00420150 --- arXiv:0909.5079 --- pdf

greenball M. Costabel: Recent progress in the analysis of the convergence of FEM for Maxwell eigenvalue problems.
(Slides from a talk at the 22nd Chemnitz FEM Symposium Oberwiesenthal, September 29, 2009)
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greenball M. Costabel, M. Dauge, S. Nicaise: Analysis of Weighted Sobolev Spaces with Nonhomogeneous Norms on Cones. (2009)
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greenball M. Costabel, A. McIntosh: On Bogovskiĭ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains. (2008, published 2010)
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greenball M. Costabel: The volume integral equation in time-harmonic dielectric scattering.
(Slides from a talk at the Workshop "BEM on the Saar". Saarbrücken University May 2008)
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greenball M. Costabel, E. Darrigrand, E. H. Kone: Volume and surface integral equations for electromagnetic scattering by a dielectric body (2007, published 2010)
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greenball M. Costabel, M. Dauge, L. Demkowicz: Polynomial extension operators for H1, Hcurl and Hdiv-spaces on a cube (2007)
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greenball M. Costabel: The biharmonic double layer potential on Lipschitz domains.
(Slides from a talk at the Conference "Mafelap", Brunel University 2006.)
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greenball M. Costabel: Some historical remarks on the positivity of boundary integral operators (2006)
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greenball M. Costabel: Anwendbare Analysis - Zum wissenschaftlichen Werk Wolfgang L. Wendlands (2004)
(Talk and slides presented 22 Oct. 2004 in Stuttgart)
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greenball Z. Yosibash, N. Omer, M. Costabel, M. Dauge: Edge stress intensity functions in polyhedral domains and their extraction by a quasidual function method (2004)
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greenball M. Costabel, M. Dauge, S. A. Nazarov, J. Sokolowski: Asymptotics near crack tips in hereditarily-elastic anisotropic aging two-dimensional body (2004)
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greenball D. Boffi, M. Costabel, M. Dauge, L. Demkowicz: Discrete compactness for the hp version of rectangular edge finite elements (2004)
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greenball M. Costabel, M. Dauge, C. Schwab: Exponential Convergence of hp-FEM for Maxwell's Equations with Weighted Regularization in Polygonal Domains (2004)
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greenball G. Caloz, M. Costabel, M. Dauge, G. Vial: Asymptotic expansion of the solution of an interface problem in a polygonal domain with thin layer (2004)
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greenball M. Costabel, M. Dauge, Z. Yosibash: A quasidual function method for extracting edge stress intensity functions (2004)
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greenball N. Omer, Z. Yosibash, M. Costabel, M. Dauge: Edge flux intensity functions in polyhedral domains and their extraction by a quasidual function method (2004)
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greenball M. Costabel: Time-dependent problems with the boundary integral equation method (2003)
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greenball A. Buffa, M. Costabel, M. Dauge: Algebraic convergence for anisotropic edge elements in polyhedral domains (2003)
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greenball M. Costabel, M. Dauge, S. Nicaise: Corner singularities of Maxwell interface and eddy current problems (2003)
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greenball M. Costabel, M. Dauge, S. Nicaise: Singularities of of eddy current problems (2003)
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greenball A. Buffa, M. Costabel, M. Dauge: Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron (2003)
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greenball M. Costabel, M. Dauge: Computation of resonance frequencies for Maxwell equations in non smooth domains
(Survey article 2002)
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greenball M. Costabel, M. Dauge: The hp version of the Weighted Regularization Method for Maxwell Equations
(Slides from a talk at the LMS Durham Symposium: Computational methods for wave propagation in direct scattering. 15-25 July 2002, Durham, UK)
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greenball A. Buffa, M. Costabel, D. Sheen: On traces for H(curl,Ω) in Lipschitz domains (2002)
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greenball M. Costabel, M. Dauge, R. Duduchava: Asymptotics without logarithmic terms for crack problems (2001)
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greenball M. Costabel, M. Dauge, D. Martin, G. Vial: Weighted Regularization of Maxwell Equations -- Computations in Curvilinear Polygons (2001)
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greenball M. Costabel, C. Safa: A wavelet approximation method for the integral equations of an antenna problem
(Slides from a talk at ENUMATH01, 26/7/2001, Ischia)
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greenball M. Costabel, M. Dauge: Weighted Regularization of Maxwell Equations in Polyhedral Domains (2001)
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Slides: Standard Finite Elements and Weighted Regularization: A Rehabilitation.
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greenball M. Costabel, M. Dauge: Crack singularities for general elliptic systems (1999)
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greenball M. Costabel, M. Dauge, D. Martin: Numerical investigation of a boundary penalization method for Maxwell equations (1999)
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greenball M. Costabel, J. Saranen: Spline Collocation for Convolutional Parabolic Boundary Integral Equations (1998)
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greenball M. Costabel, M. Dauge, Y. Lafranche: A fast semi-analytic method for the computation of elastic edge singularities (1998)
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greenball M. Costabel, M. Dauge: Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien (1998)
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greenball M. Costabel, M. Dauge, S. Nicaise: Singularities of Maxwell interface problems (1998)
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greenball M. Costabel, M. Dauge: Maxwell and Lamé Eigenvalues on Polyhedra (1998)
--- Abstract --- pdf --- ps.gz

greenball M. Costabel, M. Dauge: Singularities of electromagnetic fields in polyhedral domains
Preprint IRMAR (1997) --- Abstract --- ps --- ps.gz
Published version (2000) : ps --- ps.gz --- SpringerLINK

greenball M. Costabel, M. Dauge: Singularités des équations de Maxwell dans un polyèdre (1997)
--- Abstract --- pdf

greenball M. Costabel: Corner and Edge Singularities: A Closer Look at Parameter Dependence and Variable Coefficients
(Plenary talk at the 1997 GAMM conference)
Transparencies --- pdf
Literature list on singularities --- pdf --- ps.gz

greenball M. Costabel, M. Dauge: Invertibility of the biharmonic single layer potential operator (1996)
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greenball M. Costabel: Developments in Time Dependent Boundary Element Methods (1994)
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greenball M. Costabel: A Coercive Bilinear Form for Maxwell's Equations (1991)
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greenball M. Costabel: A Remark on the Regularity of Maxwell's Equations on Lipschitz Domains (1990)
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greenball M. Costabel: Boundary integral operators for the heat equation (1990)
--- pdf (8.5MB) --- SpringerLink

greenball M. Costabel: Boundary integral operators on Lipschitz domains: Elementary results (1988)
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greenball M. Costabel: Principles of Boundary Element Methods (1986)
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greenball M. Costabel, E. Stephan: A direct boundary integral equation method for transmission problems (1985)
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greenball M. Costabel, E. Stephan: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation (1985)
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Last modification 5 October 2012