M. Costabel:
Convergence of a simple discretization of the finite Hilbert transformation.
Computers and Mathematics with Applications 150 (2023) 15-21.
--- HAL: hal-04043771 --- arXiv: 2303.13693 --- DOI : 10.1016/j.camwa.2023.09.004
M. Costabel:
Convergence of a simple discretization of the finite Hilbert transformation.
Computers and Mathematics with Applications 150 (2023) 15-21.
--- pdf
--- HAL: hal-04043771
--- arXiv: 2303.13693
--- DOI : 10.1016/j.camwa.2023.09.004
M. Costabel, M. Dauge, Kh. Nedaiasl:
Stability Analysis of a Simple Discretization Method
for a Class of Strongly Singular Integral Equations
Integral Equations Operator Theory 95:29 (2017), 36 pages.
--- pdf
--- DOI : 10.1007/s00020-023-02750-7
--- HAL: hal-04004998
--- arXiv: 2302.13159
--- Springer SharedIt
M. Costabel:
On the stability of a delta-delta discretization of volume integral equations
(Slides from a talk at the conference in honor of the
60th birthday of Serge Nicaise,
"PDE, Analysis and Applications",
2-5 November 2021, Valenciennes, France)
--- pdf(12 MB)
M. Costabel:
On the coercivity of space-time boundary integral equations
(Slides from an online talk at the
Minisymposium in memory of Francisco-Javier Sayas,
CEDYA / CMA 2020,
June 15, 2021, Gijón, Spain and Thorigné-Fouillard, France)
--- pdf(14 MB)
M. Costabel:
Sharp regularity results for electromagnetic fields in Lipschitz domains
(Slides from a talk at the Online
Tbilisi Analysis & PDE Seminar
March 22, 2021, Tbilisi, Georgia and Thorigné-Fouillard, France)
--- pdf(31.2 MB)
M. Costabel, M. Dauge, J-Q. Hu:
Characterization of Sobolev spaces by their Fourier coefficients in axisymmetric domains.
Calcolo 60:15 (2023), 1-37
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--- HAL: hal-02500415
--- arXiv : 2004.07216
--- DOI : 10.1007/s10092-023-00504-w
M. Costabel:
Spectral Properties of the Double Layer Potential
(Slides from a talk at
The Ninth Congress of Romanian Mathematicians
June 28 - July 3, 2019, Galați, Romania)
--- pdf(10.5 MB)
M. Costabel:
On the limit Sobolev regularity for Dirichlet and Neumann problems on Lipschitz domains.
Math. Nachr. 292 (2019), 2165-2173
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--- HAL: hal-01638088
--- arXiv : 1711.07179
--- DOI : 10.1002/mana.201800077
M. Costabel:
3x60 Years of Integral Equation Methods
(Slides from a talk at the conference
"Waves Diffracted by Patrick Joly",
Saclay, 28–30 August 2017)
--- pdf(790kB)
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
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)
--- pdf(1.3MB)
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.
--- pdf
--- HAL: hal-01215296
--- arXiv : 1510.03978
M. Costabel:
Inequalities of Babuška-Aziz and Friedrichs-Velte for differential forms.
Operator Theory: Advances and Applications, Vol. 258, 79-88.
Springer International Publishing 2017.
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--- HAL: hal-01181963
--- arXiv:1507.08464
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.
--- pdf
--- HAL: hal-01145730
--- arXiv:1505.05429
--- DOI : 10.1016/j.camwa.2015.08.026
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
M. Costabel:
On the Method of Volume Integral Equations
(Slides from a plenary talk at IMSE 2014, Karlsruhe 21-25 July 2014)
--- pdf(6.8MB)
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)
--- pdf(2.7MB)
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
M. Costabel:
The inf-sup constant of the divergence.
(Slides from a plenary talk at MAFELAP 2013, Uxbridge 14/06/2013)
--- pdf(5MB)
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
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
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
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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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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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
M. Costabel, A. McIntosh, R. J. Taggart:
Potential maps and Hardy spaces on special Lipschitz domains.
(2010)
--- HAL: hal-00490854
--- arXiv:1006.0562
M. Costabel, M. Dauge, S. Nicaise:
Analytic regularity for linear elliptic systems in polygons and polyhedra
(2010)
--- HAL: hal-00454133
--- arXiv:1002.1772
--- pdf
M. Costabel, F. Le Louër:
Shape derivatives of boundary integral operators in electromagnetic scattering.
(2010)
--- HAL: hal-00453948
--- pdf
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)
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
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
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)
--- Abstract
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M. Costabel, M. Dauge, S. Nicaise:
Analysis of Weighted Sobolev Spaces with Nonhomogeneous Norms on Cones.
(2009)
--- Abstract
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M. Costabel, A. McIntosh:
On Bogovskiĭ and regularized Poincaré integral operators for
de Rham complexes on Lipschitz domains.
(2008, published 2010)
--- Abstract
--- pdf
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)
--- Abstract
--- pdf
M. Costabel, E. Darrigrand, E. H. Kone:
Volume and surface integral equations for electromagnetic scattering
by a dielectric body
(2007, published 2010)
--- Abstract
--- pdf
M. Costabel, M. Dauge, L. Demkowicz:
Polynomial extension operators for H1, Hcurl and Hdiv-spaces on a cube
(2007)
--- Abstract
--- pdf
M. Costabel:
The biharmonic double layer potential on Lipschitz domains.
(Slides from a talk at the Conference "Mafelap", Brunel University 2006.)
--- Abstract
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M. Costabel:
Some historical remarks on the positivity of boundary integral operators
(2006)
--- Abstract
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M. Costabel:
Anwendbare Analysis - Zum wissenschaftlichen Werk
Wolfgang L. Wendlands
(2004)
(Talk and slides presented 22 Oct. 2004 in Stuttgart)
--- pdf (12.8 MB)
Z. Yosibash, N. Omer, M. Costabel, M. Dauge:
Edge stress intensity functions in polyhedral domains and their extraction by a quasidual function method
(2004)
--- Abstract
--- pdf
M. Costabel, M. Dauge, S. A. Nazarov, J. Sokolowski:
Asymptotics near crack tips in hereditarily-elastic anisotropic aging
two-dimensional body
(2004)
--- Abstract
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D. Boffi, M. Costabel, M. Dauge, L. Demkowicz:
Discrete compactness for the hp version of rectangular edge
finite elements
(2004)
--- Abstract
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M. Costabel, M. Dauge, C. Schwab:
Exponential Convergence of hp-FEM
for Maxwell's Equations with Weighted Regularization
in Polygonal Domains
(2004)
--- Abstract
--- pdf
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)
--- Abstract
--- pdf
M. Costabel, M. Dauge, Z. Yosibash:
A quasidual function method for extracting edge stress intensity functions
(2004)
--- Abstract
--- pdf
N. Omer, Z. Yosibash, M. Costabel, M. Dauge:
Edge flux intensity functions in polyhedral domains and their extraction by a quasidual function method
(2004)
--- Abstract
--- pdf
M. Costabel:
Time-dependent problems with the boundary integral equation method
(2003)
--- Abstract
--- pdf
A. Buffa, M. Costabel, M. Dauge:
Algebraic convergence for anisotropic edge elements in polyhedral domains
(2003)
--- Abstract
--- pdf
M. Costabel, M. Dauge, S. Nicaise:
Corner singularities of Maxwell interface and eddy current problems
(2003)
--- Abstract
--- pdf
M. Costabel, M. Dauge, S. Nicaise:
Singularities of of eddy current problems
(2003)
--- Abstract
--- pdf
A. Buffa, M. Costabel, M. Dauge:
Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron
(2003)
--- Abstract
--- pdf
M. Costabel, M. Dauge:
Computation of resonance frequencies for Maxwell equations in non smooth domains
(Survey article 2002)
--- Abstract
--- pdf
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)
--- Abstract
--- pdf
A. Buffa, M. Costabel, D. Sheen:
On traces for H(curl,Ω) in Lipschitz domains
(2002)
--- Abstract
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A. Buffa, M. Costabel, C. Schwab:
Boundary element methods for Maxwell's equations on non-smooth
domains
(2002)
--- Abstract
--- pdf
M. Costabel, M. Dauge, R. Duduchava:
Asymptotics without logarithmic terms for crack problems
(2001)
--- Abstract
--- pdf
M. Costabel, M. Dauge, D. Martin, G. Vial:
Weighted Regularization of Maxwell Equations --
Computations in Curvilinear Polygons
(2001)
--- Abstract
--- pdf
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)
--- Abstract
--- pdf
M. Costabel, M. Dauge:
Weighted Regularization of Maxwell Equations in Polyhedral Domains
(2001)
--- Abstract
--- pdf
Slides:
Standard Finite Elements and Weighted Regularization:
A Rehabilitation.
--- pdf
M. Costabel, M. Dauge:
Crack singularities for general elliptic systems
(1999)
--- Abstract
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M. Costabel, M. Dauge, D. Martin:
Numerical investigation of a boundary penalization method for
Maxwell equations
(1999)
--- Abstract
--- pdf
M. Costabel, J. Saranen:
Spline Collocation for Convolutional Parabolic
Boundary Integral Equations
(1998)
--- Abstract
--- pdf
M. Costabel, M. Dauge, Y. Lafranche:
A fast semi-analytic method for the computation of elastic edge singularities
(1998)
--- Abstract
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M. Costabel, M. Dauge:
Un résultat de densité pour les équations de Maxwell
régularisées dans un domaine lipschitzien
(1998)
--- Abstract
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M. Costabel, M. Dauge, S. Nicaise:
Singularities of Maxwell interface problems
(1998)
--- Abstract
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M. Costabel, M. Dauge:
Maxwell and Lamé Eigenvalues on Polyhedra
(1998)
--- Abstract
--- pdf
--- ps.gz
M. Costabel, M. Dauge:
Singularities of electromagnetic fields in polyhedral domains
Preprint IRMAR (1997)
--- Abstract
--- ps
--- ps.gz
Published version (2000) :
ps
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--- SpringerLINK
M. Costabel, M. Dauge:
Singularités des équations de Maxwell dans un polyèdre
(1997)
--- Abstract
--- pdf
M. Costabel:
Corner and Edge Singularities: A Closer Look at Parameter Dependence
and Variable Coefficients
(Plenary talk at the 1997 GAMM conference)
Transparencies
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Literature list on singularities
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M. Costabel, M. Dauge:
Invertibility of the biharmonic single layer potential operator
(1996)
--- Abstract
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M. Costabel:
Developments in Time Dependent Boundary Element Methods
(1994)
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M. Costabel:
A Coercive Bilinear Form for Maxwell's Equations
(1991)
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M. Costabel:
A Remark on the Regularity of Maxwell's Equations on Lipschitz
Domains
(1990)
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M. Costabel:
Boundary integral operators for the heat equation
(1990)
--- pdf (8.5MB)
--- SpringerLink
M. Costabel, E. Stephan:
Strongly elliptic boundary integral equations for electromagnetic
transmission problems.
(1988)
--- pdf
M. Costabel:
Boundary integral operators on Lipschitz domains: Elementary results
(1988)
--- pdf
M. Costabel:
Principles of Boundary Element Methods
(1986)
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M. Costabel, E. Stephan:
A direct boundary integral equation method
for transmission problems
(1985)
--- pdf (2.2MB)
M. Costabel, E. Stephan:
Boundary integral equations for mixed boundary value problems in
polygonal domains and Galerkin approximation
(1985)
--- pdf (6.5MB)