Remarques sur les algorithmes de décomposition de domaines

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1. Y. Achdou et F. Nataf. Preconditionners for mortar methods based on local approximations of the Steklov-Poincarré operator. M3AS, 5(7) :967–997, 1995. Zbl0838.76036MR1359216
2. P. Chevalier et F. Nataf. Symmetrized method with optimized second-order conditions for the Helmholtz equation. In Domain Decomposition 10, volume 218 of Contemporary Mathematics, pages 400–407, 1998. Zbl0909.65105MR1649636
3. R. Courant et D. Hilbert. Methods of Mathematical Physics II. New York-London, Interscience Publishers, 1962. Zbl0099.29504
4. M. Dauge. Elliptic Boundary Value Problems on Corner Domains, volume 1341 of Lect. Notes Math. Springer, 1988. Zbl0668.35001MR961439
5. L. Boutet de Monvel. Boundary value problems for pseudo-differential operators. Acta Math, 126 :11–51, 1971. Zbl0206.39401MR407904
6. B. Desprès. Décomposition de domaine et problème de Helmholtz. C.R. Acad. Sci., 311 :313–316, 1990. Zbl0729.35035MR1071633
7. F.R. Gantmacher. The Theory of Matrices. Chelsea Publishing Co., 959. 2 vol. Zbl0927.15002
8. P. Grisvard. Singularities in Boundary Value Problems. Masson, Springer, 1992. Zbl0766.35001MR1173209
9. G. Grubb. Functional Calculus of Pseudodifferential Boundary Problems, volume 65 of Progress in Mathematics. Basel : Birkhaeuser, 1996. Zbl0844.35002MR1385196
10. T. Hagstrom, A. Jazcilevich et R.P. Tewarson. Numerical experiments on a domain decomposition algorithm for nonlinear elliptic boundary value problems. Appl. Math. Lett., 1(3) :299–302, 1988. Zbl0656.65097MR963704
11. N. Jacobson. Basic Algebra. Freeman, 1985. 2 vol. Zbl0441.16001MR780184
12. C. Japhet. Méthode de décomposition de domaine et conditions aux limites artificielles en mécanique des fluides : méthode optimisée d’ordre 2. Thèse de l’Université Paris 13, 1998. 
13. V.A Kondratiev. Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov Mat. Ob.v s.v c., 16 :209–292, 1967. Zbl0194.13405MR226187
14. P.L. Lions. On the Schwarz alternating method I. In First International Symposium on Domain Decomposition Methods. SIAM, 1988. Zbl0658.65090MR972510
15. P.L. Lions. On the Schwarz alternating method II : Stochastic Interpretation and Order Properties. In Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 47–70. SIAM, 1989. Zbl0681.65072MR992003
16. P.L. Lions. On the Schwarz alternating method III : A variant for nonoverlapping subdomains. In Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 202–223. SIAM, 1989. Zbl0704.65090MR1064345
17. F. Nataf. Conditions d’interface pour les méthodes de décomposition de domaine pour le système d’Oseen en dimension 2 et 3. C.R. Acad. Sci. Paris Sér. I Math., 324(10) :1155–1160, 1997. Zbl0877.65078
18. F. Nataf. A Schwarz additive method with high order interface conditions and nonoverlapping subdomains. RAIRO M2AN, 32(32) :107–116, 1998. Zbl0926.65098MR1619596
19. F. Nataf et F. Nier. Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains. Numerische Mathematik, 75(3) :357–377, 1997. Zbl0873.65108MR1427713
20. F. Nataf et F. Nier. Convergence of domain decomposition methods via semi-classical calculus. Comm. Partial Differential Equations, 23(5–6) :1007–1059, 1998. Zbl0909.35007MR1632788
21. F. Nataf et F. Rogier. Factorization of the convection-diffusion operator and the Schwarz algorithm. M${}^3$AS, 5(1) :67–93, 1995. Zbl0826.65102MR1314997
22. F. Nataf, F. Rogier, et E. de Sturler. Domain decomposition methods for fluid dynamics. In Navier Stokes equations and related non linear analysis, pages 307–377. Plenum Press Corporation, 1995. Zbl0861.76070MR1373229
23. E. Schrohe et B.W. Schulze. Boundary value problems in Boutet de Monvel’s algebra for manifolds with conical singularities I. In Pseudo-differential calculus and mathematical physics, Math. Top. 5, pages 97–209. Akademie Verlag, 1994. Zbl0827.35145
24. E. Schrohe et B.W. Schulze. Boundary value problems in Boutet de Monvel’s algebra for manifolds with conical singularities II. In Boundary value problems, Schrödinger operators, deformation, Math. Top. 8, pages 70–205. Akademie Verlag, 1995. Zbl0847.35156
25. G. Shimura. Introduction to the Arithmetic Theory of Automorphic Functions. Number 11 in Publications of Mathematical Society of Japan. Iwanami Shoten, 1971. Zbl0221.10029MR314766
26. M.A. Shubin. Spectra of elliptic operators on non compact manifolds. In Méthodes semi-classiques, Ecole d’Été Nantes, juin 1991, volume 207 of Astérisque, pages 35–108. SMF, 1992. Zbl0793.58039
27. J. Weyman. The equations of conjugacy classes of nilpotent matrices. Inventiones Mathematicae, 98 :229–245, 1989. Zbl0717.20033MR1016262

1. Chokri Chniti, A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients
2. Chokri Chniti, A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients