Multigrid methods for parameter dependent problems
Brenner, Susanne C.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996), p. 265-297 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1996__30_3_265_0,
     author = {Brenner, Susanne C.},
     title = {Multigrid methods for parameter dependent problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {30},
     year = {1996},
     pages = {265-297},
     mrnumber = {1391708},
     zbl = {0848.73062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1996__30_3_265_0}
}

Brenner, Susanne C. Multigrid methods for parameter dependent problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996) pp. 265-297. http://gdmltest.u-ga.fr/item/M2AN_1996__30_3_265_0/

[1] D. N. Arnold, 1981, Discretization by finite elements of a parameter dependent problem, Numer. Math., 37, pp. 405-421. | MR 627113 | Zbl 0446.73066

[2] D. N. Arnold, F. Brezzi and M. Fortin, 1984, A stable finite element for the Stokes equations, Calcolo, 21, pp. 337-344. | MR 799997 | Zbl 0593.76039

[3] 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. | MR 1025088 | Zbl 0696.73040

[4] D. N. Arnold and R. S. Falk, 1990, The boundary layer for the Reissner-Mindlin plate model, SIAM J. Math. Anal, 21, pp. 281-312. | MR 1038893 | Zbl 0698.73042

[5] R. E. Bank and T. Dupont, 1981, An optimal order process for solving finite element equations, Math, Comp., 36, pp. 35-51. | MR 595040 | Zbl 0466.65059

[6] D. Braess and C. Blömer, 1990, A multigrid method for a parameter dependent problem in solid mechanics, Numer. Math., 57, pp. 747-761. | MR 1065522 | Zbl 0665.65077

[7] D. Braess and R. Verfürth, 1990, Multigrid methods for nonconforming finite element methods, SIAM J. Numer. Anal, 27, pp. 979-986. | MR 1051117 | Zbl 0703.65067

[8] J. H. Bramble, 1993, Multigrid Methods, Longman Scientific & Technical, Essex. | MR 1247694 | Zbl 0786.65094

[9] S. C. Brenner, 1989, An optimal order multigrid method for PI nonconforming finite elements, Math. Comp., 52, pp. 1-15. | MR 946598 | Zbl 0664.65103

[10] S. C. Brenner, 1989, Multigrid methods for nonconforming finite elements, in Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods, J. Mandel et al, ed., Society for Industrial and Applied Mathematics, Philadelphia, pp. 54-65. | MR 1065626

[11] S. C. Brenner, 1990, A nonconforming multigrid method for the stationary Stokes equations, Math. Comp., 55, 1993, pp. 411-437. | MR 1035927 | Zbl 0705.76027

[12] S. C. Brenner, 1993, A nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity, SIAM J. Numer. Anal, 30,pp. 116-135. | MR 1202659 | Zbl 0767.73068

[13] S. C. Brenner, 1994, A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticity, Math. Comp., 63, pp. 435-460, S1-S5. | MR 1257574 | Zbl 0809.73064

[14] S. C. Brenner and L. R. Scott, 1994, The Mathematical Theory of Finite Element Methods, Springer-Verlag. | MR 1278258 | Zbl 0804.65101

[15] S. C. Brenner and L.-Y. Sung, 1992, Linear finite element methods for planar linear elasticity, Math. Comp., 59, pp. 321-338. | MR 1140646 | Zbl 0766.73060

[16] F. Brezzi, K. J. Bathe and M. Fortin, 1989, Mixed-interpolated elements for Reissner-Mindlin plates, Int. J. Numer. Math, Eng., 28, pp. 1787-1801. | MR 1008138 | Zbl 0705.73238

[17] F. Brezzi and M. Fortin, 1986, Numerical approximation of Mindlin-Reissner plates, Math. Comp., 47, pp. 151-158. | MR 842127 | Zbl 0596.73058

[18] F. Brezzi and M. Fortin, 1991, Mixed and Hybrid Finite Element Methods, Springer-Verlag. | MR 1115205 | Zbl 0788.73002

[19] F. Brezzi, M. Fortin and R. Stenberg, 1991, Error analysis of mixed-interpolated elements for Reissner-Mindlin plates, Math. Models and Methods in Appl. Sci., 1, pp. 125-151. | MR 1115287 | Zbl 0751.73053

[20] M. Crouzeix and P.-A. Raviart, 1973, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, R.A.I.R.O., R-3, pp. 33-75. | Numdam | MR 343661 | Zbl 0302.65087

[21] P. G. Ciarlet, 1978, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam-New York-Oxford. | MR 520174 | Zbl 0383.65058

[22] R. Durán and E. Lieberman, 1992, On mixed finite element methods for the Reissner-Mindlin plate model, Math. Comp., 58, pp. 561-573. | MR 1106965 | Zbl 0763.73054

[23] R. S. Falk, 1991, Nonconforming finite element methods for the equations of linear elasticity, Math. Comp., 57, pp. 529-550. | MR 1094947 | Zbl 0747.73044

[24] W. Hackbusch, 1985, Multi-Grid Methods and Applications, Springer-Verlag, Heidelberg. | MR 833988 | Zbl 0595.65106

[25] W. Hackbusch, 1980, Analysis and multigrid solutions of mixed finite element and mixed difference equations, Report, Ruhr-Universität Bochum.

[26] H. Han, 1986, An analysis of penalty-nonconforming finite element method for Stokes equations, J Comput. Math., 4, pp. 164-172. | MR 854393 | Zbl 0623.76020

[27] Z. Huang, 1990, A multi-grid algorithm for mixed problems with penalty, Numer. Math., 57, pp. 227-247. | MR 1057122 | Zbl 0712.73106

[28] M. Jung, 1987, Konvergenzfaktoren für Mehrgitterverfahren zur Lösung von Problemen der Ebenen, Linearen Elastizitatstheorie, ZAMM, 67, pp. 165-173. | MR 887522 | Zbl 0619.73086

[29] S. Mccormlck ed., 1987, Multigrid Methods, SIAM Frontiers in Applied Mathematics 3, Society for Industrial and Applied Mathematics, Philadelphia. | MR 972752 | Zbl 0659.65094

[30] I. D. Parsons and J. F. Hall, 1990, The multigrid method in solid mechanics; part I - algorithm description and behaviour, Int. J. Numer. Meth. Engrg., 29, pp. 719-738. | Zbl 0724.73269

[31] P. Peisker, 1991, A multigrid method for Reissner-Mindlin plates, Numer. Math., 59, pp. 511-528. | MR 1121656 | Zbl 0736.73071

[32] P. Peisker and D. Braess, 1992, Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates, M2AN, 26, pp. 557-574. | Numdam | MR 1177387 | Zbl 0758.73050

[33] P. Peisker, W. Rust and E. Stein, 1990, Iterative solution methods for plate bending problems : multigrid and preconditioned cg algorithm, SIAM J. Numer. Anal, 27, pp. 1450-1465. | MR 1080331 | Zbl 0721.73040

[34] R. Verfürth, 1984, A multilevel algorithm for mixed problems, SIAM J. Numer. Anal, 21, pp. 264-271. | MR 736330 | Zbl 0534.65065

[35] R. Verfürth, 1988, Multi-level algorithms for mixed problems II, treatment of the mini-clement, SIAM J. Numer. Anal, 25, pp. 285-293. | MR 933725 | Zbl 0669.65083

[36] S. Zhang and Z. Zhang, 1991, Treatment of discontinuity and bublle functions in multigrid methods II, Technical Report 153, Center for Applied Mathematics, Purdue University.