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All issues Volume 44 / No 1 (January-February 2010) ESAIM: M2AN, 44 1 (2010) 75-108 References
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Issue
ESAIM: M2AN
Volume 44, Number 1, January-February 2010
Page(s) 75 - 108
DOI https://doi.org/10.1051/m2an/2009041
Published online 03 November 2009
  1. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains. Math. Meth. Appl. Sci. 21 (1998) 823–864. [Google Scholar]
  2. F. Assous, P. Degond, E. Heintzé, P.-A. Raviart and J. Segré, On a finite element method for solving the three-dimensional Maxwell equations. J. Comput. Phys. 109 (1993) 222–237. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Assous, P. Degond and J. Segré, Numerical approximation of the Maxwell equations in inhomogeneous media by a P1 conforming finite element method. J. Comput. Phys. 128 (1996) 363–380. [CrossRef] [MathSciNet] [Google Scholar]
  4. F. Assous, P. Ciarlet Jr. and E. Sonnendrücker, Resolution of the Maxwell equations in a domain with reentrant corners. Math. Mod. Num. Anal. 32 (1998) 359–389. [Google Scholar]
  5. F. Assous, P. Ciarlet Jr., P.-A. Raviart and E. Sonnendrücker, A characterization of the singular part of the solution to Maxwell's equations in a polyhedral domain. Math. Meth. Appl. Sci. 22 (1999) 485–499. [CrossRef] [Google Scholar]
  6. F. Assous, P. Ciarlet Jr. and J. Segré, Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: the singular complement method. J. Comput. Phys. 161 (2000) 218–249. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Birman and M. Solomyak, L2-theory of the Maxwell operator in arbitrary domains. Russ. Math. Surv. 42 (1987) 75–96. [Google Scholar]
  8. M. Birman and M. Solomyak, On the main singularities of the electric component of the electro-magnetic field in regions with screens. St. Petersbg. Math. J. 5 (1993) 125–139. [Google Scholar]
  9. D. Boffi, F. Brezzi and L. Gastaldi, On the convergence of eigenvalues for mixed formulations. Annali Sc. Norm. Sup. Pisa Cl. Sci. 25 (1997) 131–154. [Google Scholar]
  10. A.-S. Bonnet-Ben Dhia, C. Hazard and S. Lohrengel, A singular field method for the solution of Maxwell's equations in polyhedral domains. SIAM J. Appl. Math. 59 (1999) 2028–2044. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Buffa, P. Ciarlet Jr. and E. Jamelot, Solving electromagnetic eigenvalue problems in polyhedral domains. Numer. Math. 113 (2009) 497–518. [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Ciarlet Jr., Augmented formulations for solving Maxwell equations. Comp. Meth. Appl. Mech. Eng. 194 (2005) 559–586. [Google Scholar]
  13. P. Ciarlet Jr. and G. Hechme, Computing electromagnetic eigenmodes with continuous Galerkin approximations. Comp. Meth. Appl. Mech. Eng. 198 (2008) 358–365. [Google Scholar]
  14. P. Ciarlet Jr. and G. Hechme, Mixed, augmented variational formulations for Maxwell's equations: Numerical analysis via the macroelement technique. Numer. Math. (Submitted). [Google Scholar]
  15. P. Ciarlet Jr., C. Hazard and S. Lohrengel, Les équations de Maxwell dans un polyèdre : un résultat de densité. C. R. Acad. Sci. Paris, Ser. I 326 (1998) 1305–1310. [Google Scholar]
  16. M. Costabel and M. Dauge, Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien. C. R. Acad. Sci. Paris, Ser. I 327 (1998) 849–854. [Google Scholar]
  17. M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains. Arch. Rational Mech. Anal. 151 (2000) 221–276. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Costabel and M. Dauge, Weighted regularization of Maxwell's equations in polyhedral domains. Numer. Math. 93 (2002) 239–277. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Costabel, M. Dauge and S. Nicaise, Singularities of Maxwell interface problems. ESAIM: M2AN 33 (1999) 627–649. [CrossRef] [EDP Sciences] [Google Scholar]
  20. M. Dauge, Benchmark computations for Maxwell equations for the approximation of highly singular solutions. (2004). See Monique Dauge's personal web page at the location http://perso.univ-rennes1.fr/monique.dauge/core/index.html [Google Scholar]
  21. P. Fernandes and G. Gilardi, Magnetostatic and electrostatic problems in inhomogeneous anisotropic media with irregular boundary and mixed boundary conditions. Math. Models Meth. Appl. Sci. 7 (1997) 957–991. [CrossRef] [Google Scholar]
  22. P. Grisvard, Edge behaviour of the solution of an elliptic problem. Math. Nachr. 132 (1987) 281–299. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Grisvard, Singularities in boundary value problems, RMA 22. Masson (1992). [Google Scholar]
  24. C. Hazard and M. Lenoir, On the solution of time-harmonic scattering problems for Maxwell's equations. SIAM J. Math. Anal. 27 (1996) 1597–1630. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Hazard and S. Lohrengel, A singular field method for Maxwell's equations: numerical aspects for 2D magnetostatics. SIAM J. Numer. Anal. 40 (2002) 1021–1040. [CrossRef] [MathSciNet] [Google Scholar]
  26. B. Heinrich, S. Nicaise and B. Weber, Elliptic interface problems in axisymmetric domains. I: Singular functions of non-tensorial type. Math. Nachr. 186 (1997) 147–165. [CrossRef] [MathSciNet] [Google Scholar]
  27. D. Leguillon and E. Sanchez-Palencia, Computation of singular solutions in elliptic problems and elasticity, RMA 5. Masson (1987). [Google Scholar]
  28. S. Lohrengel and S. Nicaise, Singularities and density problems for composite materials in electromagnetism. Comm. Partial Diff. Eq. 27 (2002) 1575–1623. [CrossRef] [Google Scholar]
  29. J.M.-S. Lubuma and S. Nicaise, Dirichlet problems in polyhedral domains. I: Regularity of the solutions. Math. Nachr. 168 (1994) 243–261. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Monk, Finite element methods for Maxwell's equations. Oxford University Press, UK (2003). [Google Scholar]
  31. M. Moussaoui, Formula dans un polygone plan. C. R. Acad. Sci. Paris, Ser. I 322 (1996) 225–229. [Google Scholar]
  32. S. Nazarov and B. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries, Exposition in Mathematics 13. De Gruyter, Berlin, Germany (1994). [Google Scholar]
  33. S. Nicaise, Polygonal interface problems. Peter Lang, Berlin, Germany (1993). [Google Scholar]
  34. S. Nicaise and A.-M. Sändig, General interface problems I, II. Math. Meth. Appl. Sci. 17 (1994) 395–450. [CrossRef] [MathSciNet] [Google Scholar]
  35. B. Smith, P. Bjorstad and W. Gropp, Domain decomposition. Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, New York, USA (1996). [Google Scholar]

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