no. 4
Preconditioning discrete approximations of the Reissner-Mindlin plate model
ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 4, pp. 517-557 
@article{M2AN_1997__31_4_517_0,
     author = {Arnold, Douglas N. and Falk, Richard S. and Winther, Ragnar},
     title = {Preconditioning discrete approximations of the {Reissner-Mindlin} plate model},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {517--557},
     year = {1997},
     publisher = {Elsevier},
     volume = {31},
     number = {4},
     mrnumber = {1457459},
     zbl = {0877.73060},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1997__31_4_517_0/}
}
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Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar. Preconditioning discrete approximations of the Reissner-Mindlin plate model. ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 4, pp. 517-557. https://www.numdam.org/item/M2AN_1997__31_4_517_0/

[1] D. N. Arnold and R. S. Falk, 1989, A uniformly accurate finite element method for the Reissner-Mindlin plate, SIAM J. Numer. Anal. 26, pp 1276-1290. | Zbl | MR

[2]J. Bergh and J. Löfstrom, 1976, Interpolation spaces, an introduction, Springer Verlag. | Zbl | MR

[3] D. Braess and C. Blömer, 1990, A multigrid method for a parameter dependent problem in solid mechanics, Numer. Math. 57., pp. 747-762. | Zbl | MR

[4] J. H. Bramble and J. E. Pasciak, 1988, A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comp., 50, pp. 1-17. | Zbl | MR

[5] J. H. Bramble and J. E. Pasciak, Iterative techniques for time dependent Stokes problem, to appear in Comput. Math. Appl. | Zbl | MR

[6] J. H. Bramble, J. E. Pasciak and A. T. Vassilev, Analysis of inexact Uzawa algorithm for saddle point problems, to appear in SIAM J. Numer. Anal. | Zbl | MR

[7] J. H. Bramble, J. E. Pasciak and J. Xu, 1991, The analysis of multigrid algorithms with nonnested spaces and noninherited quadratic forms, Math. Comp., 56, pp. 1-34. | Zbl | MR

[8] S. C. Brenner, 1996, Multigrid methods for parameter dependent problems, to appear in Math. Modelling Numer. Anal, 30, pp. 265-297. | Zbl | MR | Numdam

[9] F. Brezzi, M. Fortin and R. Stenberg, 1991, Error analysis of mixed-interpolated elements for Reissner-Mindlin plates, Math. Models and Methods in Applied Sciences, 1, pp. 125-151. | Zbl | MR

[10] L. C. Cowsar, 1993, Dual variable Schwarz methods for mixed finite elements, Report TR93-09, Riee University, Houston.

[11] L. C. Cowsar, J. Mandel and M. F. Wheeler, 1995, Balancing domain decomposition for mixed finite elements, Math. Comp., 64, pp. 989-1015. | Zbl | MR

[12] R. Durán and E. Liberman, 1992 On mixed finite element methods for the Reissner-Mindlin plate model, Math. Comp., 58, pp.561-573. | Zbl | MR

[13] H. C. Elman and G. Golub, 1994, Inexact and preconditioned Uzawa algorithms for saddle point problems, SIAM J. Numer. Anal., 31, pp. 1645-1661. | Zbl | MR

[14] W. Hackbusch, 1994, Iterative solution of large sparse Systems of equations, Springer Verlag. | Zbl | MR

[15] Z. Huang, 1990, A multi-grid algorithm for mixed problems with penalty, Numer. Math., 57, pp. 227-247. | Zbl | MR

[16] A. Klawonn, 1994, An optimal preconditioner for a class of saddle point problems with a penalty term, Preprint. | Zbl | MR

[17] P. Peisker, 1991, A multigrid method for Reissner-Mindlin plates, Numer. Math., 59, pp. 511-528. | Zbl | MR

[18] T. Rusten P. S. Vassilevski and R. Wïnther, 1996, Interior penalty preconditioners for mixed finite element approximations of elliptic problems, Math. Comp., 65, pp.447-466. | Zbl | MR

[19] T. Rusten and R. Wïnther, 1992, A preconditioned iterative method for saddle point problems, SIAM J. Matrix Anal. Appl., 13, pp. 887-904. | Zbl | MR

[20] T. Rusten and R. Winther, 1993, Substructure preconditioners for elliptic saddle point problems, Math. Comp., 60, pp. 23-48. | Zbl | MR

[21]D. Silvester and A. Wathen, 1994, Fast iterative solution of stabilised Stokes Systems, Part II : Using general block preconditioners, SIAM J. Numer. Anal., 31, pp. 1352-1367. | Zbl | MR

[22] P. S. Vassilevski and J. Wang, 1995, An application of the abstract multilevel theory to nonconforming finite element methods, SIAM J. Numer. Anal., 32, pp. 235-248. | Zbl | MR

[23] A. Wathen, 1987, Realistic eigenvalue bounds for the Galerkin mass matrix, IMA J. Numer. Anal., 7, pp. 449-457. | Zbl | MR

[24] A. Wathen and D. Silvester, 1993, Fast iterative solution of stabilised Stokes Systems, Part I : Using simple diagonal preconditioners, SIAM J. Numer. Anal., 30, pp. 630-649. | Zbl | MR

[25] J. Xu, 1996, The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids, to appear in Computing, 56, pp. 215-235. | Zbl | MR