Resolution of the Maxwell equations in a domain with reentrant corners

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1. [1] V.I. AGOSHKOV, 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. Zbl0683.65097MR972513
2. [2] F. ASSOUS, P. Jr. CIARLET, J. SEGRÉ and E. SONNENDRÜCKER. In préparation. 
3. [3] F. ASSOUS, P. Jr. CIARLET and E. SONNENDRÜCKER, Résolution des équations de Maxwell dans un domaine avec un coin rentrant. C. R. Acad. Sc. Paris Serie I 323 (1996) 203-208. Zbl0855.65131MR1402544
4. [4] F. ASSOUS, P. Jr. CIARLET and E. SONNENDRÜCKER, 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). 
5. [5] 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. Zbl0795.65087MR1253460
6. [6] I. BABUSKA, The finite element method with Lagrange multipliers, Numer. Math., 20 (1973), 179-192. Zbl0258.65108MR359352
7. [7] I. BABUSKA, R. B. KELLOG and PITKÄRANTA, Direct and inverse error estimates for finite elements with mesh refinements, Numer. Math., 33 (1979), 447-471. Zbl0423.65057MR553353
8. [8] I. BABUSKA and H.-S. OH, 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. Zbl0717.65084MR1087251
9. [9] F. BREZZI, On the existence uniqueness and approximation of saddle point problems arising from Lagrange multipliers, RAIRO Anal. Numer. (1974), 129-151. Zbl0338.90047MR365287
10. [10] W. CAI, H. C LEE and H.-S. OH, 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. Zbl0790.65093MR1242954
11. [11] M. CESSENAT, 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. Zbl0694.35040MR1004933
12. [12] M. CESSENAT, Résolution des problèmes de Helmholtz par séparation des variables en coordonnées polaires, C. R. Acad. Sci. Paris, Série I 309 (1989), 105-109. Zbl0688.35020MR1004950
13. [13] P. Jr. CIARLET, Tools for solving the div-curl problem with mixed boundary conditions in a polygonal domain. In preparation. 
14. [14] P. Jr. CIARLET and J. ZOU, Finite Element Convergence for the Darwin Model to Maxwell's Equations, M2AN 7, 30(1996). Zbl0887.65121
15. [15] M. COSTABEL, A Remark on the Regularity of Solutions of Maxwell's Equations on Lipschitz Domains, Math. Meth. Appl. Sci. 12, 2 (1990), 365-368. Zbl0699.35028MR1048563
16. [16] M. COSTABEL, A Coercive Bilinear Form for Maxwell's Equations, J. Math. Anal. and Appl. 157, 2 (1991), 527-541. Zbl0738.35095MR1112332
17. [17] M. COSTABEL and M. DAUGE, Stable Asymptotics for Elliptic Systems on Plane Domains with Corners, Comm. PDE 19, 9 & 10 (1994), 1677-1726. Zbl0814.35024MR1294475
18. [18] C. L. COX and G. J. FIX, On the accuracy of least square methods in the presence of corner singularities, Comp. Math. Appl. 10, (1984), 463-471. Zbl0573.65081MR783520
19. [19] M. DAUGE, (1988), Elliptic boundary value problems on corner domains, Lecture Notes in Mathematics, 1341, Springer Verlag, Berlin. Zbl0668.35001MR961439
20. [20] G. J. FIX (1986), 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. Zbl0727.73070MR964480
21. [21] G. J. FIX, S. GULATI and G. I. WAKOFF, On the use of singular function with finite element approximation, J Comp. Phys. 13, (1973), 209-228. Zbl0273.35004MR356540
22. [22] P. GÉRARD and G. LEBEAU, Diffusion d'une onde par un coin, J. Amer. Math. Soc. 6 (1993), 341-424. Zbl0779.35063MR1157289
23. [23] V. GIRAULT and P.-A. RAVIART (1986), Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, Springer Verlag, Berlin. Zbl0585.65077MR851383
24. [24] D. GIVOLI, L. RIVKIN and J. B. KELLER, A Finite Element Method for Domains with Corners, Int. J. Numer. Methods Eng. 35 (1992), 1329-1345. Zbl0768.73072MR1184244
25. [25] P. GRISVARD (1985), Elliptic Problems in nonsmooth domains, Monographs and studies in Mathematics, 24, Pitman, London. Zbl0695.35060MR775683
26. [26] P. GRISVARD (1992), Singularities in boundary value problems, RMA 22, Masson, Paris. Zbl0766.35001MR1173209
27. [27] T. J. R. HUGHES and J. E. AKIN, Techniques for developing "special" finite element shape functions with particular reference to singularities, Int. J. Numer. Methods Eng. 15 (1980), 733-751. Zbl0428.73074MR580355
28. [28] J. B. KELLER and D. GIVOLI, An Exact Non-Reflecting Boundary Condition, J. Comp. Phys. 82 (1988), 172-192. Zbl0671.65094MR1005207
29. [29] O. LAFITTE, The wave diffracted by a wedge with mixed boundary conditions, SIAM Annual Meeting, Stanford (1997). Zbl0963.78018MR1635365
30. [30] O. LAFITTE, Diffraction par une arête d'une onde électromagnétique normale à l'arête, in préparation. 
31. [31] J.-L. LIONS and E. MAGENES (1968), Problèmes aux Limites Non Homogènes et Applications, Dunod, Paris. Zbl0165.10801
32. [32] M. MOUSSAOUI, Espaces H(div, curl, Ω) dans un polygone plan. C. R. Acad. Sc. Paris, Série I 322 (1996) 225-229. Zbl0852.46034MR1378257
33. [33] J. C. NÉDÉLEC, Mixed Finite Elements in R3, Numer. Math. 35 (1980), 315-341. Zbl0419.65069MR592160
34. [34] D. PATHRIA and E. KARNIADAKIS, Spectral Element Methods for Elliptic Problems in Nonsmooth Domains, J. Comput. Phys. 122 (1995), 83-95. Zbl0844.65082MR1358523
35. [35] C. WEBER, A local compactness theorem for Maxwell's equations, Math. Meth. Appl. Sci. 2 (1980), 12-25. Zbl0432.35032MR561375

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