@article{M2AN_1998__32_3_359_0, author = {Assous, F. and Ciarlet, P. and Sonnendr\"ucker, E.}, title = {Resolution of the {Maxwell} equations in a domain with reentrant corners}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {359--389}, publisher = {Elsevier}, volume = {32}, number = {3}, year = {1998}, mrnumber = {1627135}, zbl = {0924.65111}, language = {en}, url = {http://www.numdam.org/item/M2AN_1998__32_3_359_0/} }
TY - JOUR AU - Assous, F. AU - Ciarlet, P. AU - Sonnendrücker, E. TI - Resolution of the Maxwell equations in a domain with reentrant corners JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1998 SP - 359 EP - 389 VL - 32 IS - 3 PB - Elsevier UR - http://www.numdam.org/item/M2AN_1998__32_3_359_0/ LA - en ID - M2AN_1998__32_3_359_0 ER -
%0 Journal Article %A Assous, F. %A Ciarlet, P. %A Sonnendrücker, E. %T Resolution of the Maxwell equations in a domain with reentrant corners %J ESAIM: Modélisation mathématique et analyse numérique %D 1998 %P 359-389 %V 32 %N 3 %I Elsevier %U http://www.numdam.org/item/M2AN_1998__32_3_359_0/ %G en %F M2AN_1998__32_3_359_0
Assous, F.; Ciarlet, P.; Sonnendrücker, E. Resolution of the Maxwell equations in a domain with reentrant corners. ESAIM: Modélisation mathématique et analyse numérique, Volume 32 (1998) no. 3, pp. 359-389. http://www.numdam.org/item/M2AN_1998__32_3_359_0/
[1] Poincaré-Steklov's Operators and Domain Decomposition Methods in Finite Dimensional Spaces, in Glowinski, R. et al. eds, Domain Decomposition Methods for Partial Differential Equations, SIAM Philadelphia, (1988), 73-112. | MR | Zbl
,[2]
, , and . In préparation.[3] Résolution des équations de Maxwell dans un domaine avec un coin rentrant. C. R. Acad. Sc. Paris Serie I 323 (1996) 203-208. | MR | Zbl
, and ,[4] Résolution des équations de Maxwell dans un domaine 2D avec coins rentrants Partie I: Modélisation avec condition aux limites de type conducteur parfait, CEA, Technical Report, CEA-N-2813 (1996).
, and ,[5] On a Finite Element Method for Solving the Three-Dimensional Maxwell Equations, J. Comput. Phys. 109 (1993), 222-237. | MR | Zbl
, , , and ,[6] The finite element method with Lagrange multipliers, Numer. Math., 20 (1973), 179-192. | MR | Zbl
,[7] Direct and inverse error estimates for finite elements with mesh refinements, Numer. Math., 33 (1979), 447-471. | MR | Zbl
, and ,[8] The p-Version of the Finite Element Method for Domains with Corners and for Infinite Domains, Numer. Methods Partial Differential Equations, 6 (1990), 371-392. | MR | Zbl
and ,[9] On the existence uniqueness and approximation of saddle point problems arising from Lagrange multipliers, RAIRO Anal. Numer. (1974), 129-151. | Numdam | MR | Zbl
,[10] Coupling of Spectral Methods and the p-Version of the Finite Element Method for Ellitic Boundary Value Problems Containing Singularities, J. Comput. Phys. 108 (1993), 314-326. | MR | Zbl
, and ,[11] Sur quelques opérateurs liés à l'équation de Helmholtz en coordonnées polaires, transformation H.K.L., C. R. Acad. Sci. Paris, Serie I 309 (1989), 25-30. | MR | Zbl
,[12] Résolution des problèmes de Helmholtz par séparation des variables en coordonnées polaires, C. R. Acad. Sci. Paris, Série I 309 (1989), 105-109. | MR | Zbl
,[13] Tools for solving the div-curl problem with mixed boundary conditions in a polygonal domain. In preparation.
,[14] Finite Element Convergence for the Darwin Model to Maxwell's Equations, M2AN 7, 30(1996). | Numdam | Zbl
and ,[15] A Remark on the Regularity of Solutions of Maxwell's Equations on Lipschitz Domains, Math. Meth. Appl. Sci. 12, 2 (1990), 365-368. | MR | Zbl
,[16] A Coercive Bilinear Form for Maxwell's Equations, J. Math. Anal. and Appl. 157, 2 (1991), 527-541. | MR | Zbl
,[17] Stable Asymptotics for Elliptic Systems on Plane Domains with Corners, Comm. PDE 19, 9 & 10 (1994), 1677-1726. | MR | Zbl
and ,[18] On the accuracy of least square methods in the presence of corner singularities, Comp. Math. Appl. 10, (1984), 463-471. | MR | Zbl
and ,[19] Elliptic boundary value problems on corner domains, Lecture Notes in Mathematics, 1341, Springer Verlag, Berlin. | MR | Zbl
, (1988),[20] Singular finite element method, in D. L. Doyer, M. Y. Hussami and R. G. Voigt (eds), Proc. ICASE Finite Element Theory and Application Workshop, Hampton, Virginia, Springer Verlag, Berlin, pp. 50-66. | MR | Zbl
(1986),[21] On the use of singular function with finite element approximation, J Comp. Phys. 13, (1973), 209-228. | MR | Zbl
, and ,[22] Diffusion d'une onde par un coin, J. Amer. Math. Soc. 6 (1993), 341-424. | MR | Zbl
and ,[23] Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, Springer Verlag, Berlin. | MR | Zbl
and (1986),[24] A Finite Element Method for Domains with Corners, Int. J. Numer. Methods Eng. 35 (1992), 1329-1345. | MR | Zbl
, and ,[25] Elliptic Problems in nonsmooth domains, Monographs and studies in Mathematics, 24, Pitman, London. | MR | Zbl
(1985),[26] Singularities in boundary value problems, RMA 22, Masson, Paris. | MR | Zbl
(1992),[27] Techniques for developing "special" finite element shape functions with particular reference to singularities, Int. J. Numer. Methods Eng. 15 (1980), 733-751. | MR | Zbl
and ,[28] An Exact Non-Reflecting Boundary Condition, J. Comp. Phys. 82 (1988), 172-192. | MR | Zbl
and ,[29] The wave diffracted by a wedge with mixed boundary conditions, SIAM Annual Meeting, Stanford (1997). | MR | Zbl
,[30] Diffraction par une arête d'une onde électromagnétique normale à l'arête, in préparation.
,[31] Problèmes aux Limites Non Homogènes et Applications, Dunod, Paris. | Zbl
and (1968),[32] Espaces H(div, curl, Ω) dans un polygone plan. C. R. Acad. Sc. Paris, Série I 322 (1996) 225-229. | MR | Zbl
,[33] Mixed Finite Elements in R3, Numer. Math. 35 (1980), 315-341. | EuDML | MR | Zbl
,[34] Spectral Element Methods for Elliptic Problems in Nonsmooth Domains, J. Comput. Phys. 122 (1995), 83-95. | MR | Zbl
and ,[35] A local compactness theorem for Maxwell's equations, Math. Meth. Appl. Sci. 2 (1980), 12-25. | MR | Zbl
,