Analysis of multilevel decomposition iterative methods for mixed finite element methods
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 4, pp. 377-398. 
@article{M2AN_1994__28_4_377_0,
     author = {Ewing, R. E. and Wang, J.},
     title = {Analysis of multilevel decomposition iterative methods for mixed finite element methods},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {377--398},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {4},
     year = {1994},
     mrnumber = {1288504},
     zbl = {0823.65035},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1994__28_4_377_0/}
}
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Ewing, R. E.; Wang, J. Analysis of multilevel decomposition iterative methods for mixed finite element methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 4, pp. 377-398. http://archive.numdam.org/item/M2AN_1994__28_4_377_0/

[1] I. Babuška, 1973, The finite element method with Lagrangian multipliers, Numer, Math., 20, 179-192. | MR | Zbl

[2] R. E. Bank and T. F. Dupont, 1981, An optimal order process for solving elliptic finite element equations, Math. Comp., 36, 35-51. | MR | Zbl

[3] R. E. Bank, T. F. Dupont and H. Yserentant, 1988, The Hierarchical basis multigrid method, Numer. Math., 52, 427-458. | MR | Zbl

[4] J. H. Bramble, R. E. Ewing, J. E. Pasciak and A. H. Schatz, 1988, A preconditioning technique for the efficient solution of problems with local grid refinement, Compt. Meth. Appl. Mech. Eng., 67, 149-159. | Zbl

[5] J. H. Bramble, J. E. Pasciak, J. Wang andJ. Xu, 1991, Convergence estimates for product iterative methods with applications to domain decomposition, Math. Comp., 57, 1-22. | MR | Zbl

[6] J. H. Bramble, J. E. Pasciak, J. Wang and J. Xu, 1911, Convergence estimate for multigrid algorithms without regularity assumptions, Math. Comp., 57, 23-45. | MR | Zbl

[7] F. Brezzi, 1974, On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers, R.A.I.R.O., Anal. Numér., 2, 129-151. | Numdam | MR | Zbl

[8] F. Brezzi, J. Jr. Douglas, M. Fortin and L. D. Marini, 1987, Efficient rectangular mixed finite elements in two and three space variables, R.A.I.R.O., Anal. Numér., 21, 581-604. | Numdam | MR | Zbl

[9] F. Brezzi, J. Jr. Douglas and L. D. Marini, 1985, Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47, 217-235. | MR | Zbl

[10] J. Jr. Douglas and J. E. Roberts, Global estimates for mixed finite element methods for second order elliptic equations, Math. Comp., 45, 39-52. | MR | Zbl

[11] R. E. Ewing and J. Wang, 1992, Analysis of the Schwarz algorithm for mixed finite element methods, R.A.I.R.O. M2AN, 26, 739-756. | Numdam | MR | Zbl

[12] M. Dryja and O. Widlund, 1987, An additive variant of the Schwarz alternating method for the case of many subregions, Technical Report, Courant Institute of Mathematical Sciences, 339.

[13] M. Dryja and O Widlund, 1989, Some domain decomposition algorithms for elliptic problems, Technical Report, Courant Institute of Mathematical Sciences, 438. | MR

[14] R. Falk and J. Osborn, 1980, Error estimates for mixed methods, R.A.I.R.O., Anal. Numér., 14, 249-277. | Numdam | MR | Zbl

[15] M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O., Anal. Numér., 11, 341-354. | Numdam | MR | Zbl

[16] R. Glowinski and M. F. Wheeler, 1988, Domain decomposition and mixed finite element methods for elliptic problems, Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Dijferential Equations (R. Glowinski, G. H. Golub, G. A. Meurant and J. Périaux, eds.). | MR | Zbl

[17] W. Hackbusch, 1985, Multi-Grid Methods and Applications, Springer-Verlag, New York. | Zbl

[18] P. L. Lions, 1988, On the Schwarz alternating method, Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations (R. Glowinski, G. H. Golub, G. A. Meurant and J. Périaux, eds.). | MR | Zbl

[19] T. P. Mathew, 1989, Domain Decomposition and Iterative Refinement Methods for Mixed Finite Element Discretizations of Elliptic Problems, Ph. D. Thesis, New York University.

[20] P.-A. Raviart and J.-M. Thomas, 1977, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics (606), Springer-Verlag, Berlin and New York, 292-315. | MR | Zbl

[21] H. A. Schwarz, 1869, Über einige Abbildungsaufgaben, Ges. Math. Abh., 11, 65-83.

[22] J. Wang, 1992, Convergence analysis without regularity assumptions for multigrid algorithms based on SOR smoothing, SIAM J. Numer. Anal., 29, 987-1001. | MR | Zbl

[23] J. Wang, 1992, Convergence analysis of Schwarz algorithm and multilevel decomposition iterative methods I : selfadjoint and positive definite elliptic problems, in Iterative Methods in Linear Algebra, R. Beauwens and P. de Groen (eds.), North-Holland, Amsterdam. | MR | Zbl

[24] J. Wang, 1993, Convergence analysis of the Schwarz algorithm and multilevel decomposition iterative methods II : non-selfadjoint and indefinite elliptic problems, SIAM J. Numer. Anal., 30, 953-970. | MR | Zbl

[25] H. Yserentant, 1986, On the multi-level splitting of finite element spaces, Numer. Math., 49, 379-412. | MR | Zbl