A mixed finite element method for the biharmonic problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 14 (1980) no. 1, p. 55-79
@article{M2AN_1980__14_1_55_0,
     author = {Scapolla, T.},
     title = {A mixed finite element method for the biharmonic problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {14},
     number = {1},
     year = {1980},
     pages = {55-79},
     zbl = {0436.65088},
     mrnumber = {566090},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1980__14_1_55_0}
}
Scapolla, T. A mixed finite element method for the biharmonic problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 14 (1980) no. 1, pp. 55-79. http://www.numdam.org/item/M2AN_1980__14_1_55_0/

1. J. H. Ramble and R. S. Hilbert, Estimation of Linear Functionals on Sobolev Spaces with Applications to Fourier Transforms and Spline Interpolation, S.I.A.M. J. Numer. Anal., Vol. 7, 1970, pp. 112-124. | MR 263214 | Zbl 0201.07803

2. F. Brezzi, On the Existence Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers, R.A.I.R.O., Vol. 8, R 2, 1974, pp. 129-151 | Numdam | MR 365287 | Zbl 0338.90047

3. F. Brezzi and L. D. Marini, On the Numerical Solution of Plate Bending Problems by Hybrid Mathods, R.A.I.R.O., Vol. 9, R 3, 1975, pp.5-50. | Numdam | Zbl 0322.73048

4 F Brezzi and P A Raviart, Mixed Finite Element Methods for 4th Order Elliptic Equations, Proc of the Royal Insh Academy Conference on Numencal Analysis, 1976, Academic Press, London, 1977 | MR 657975 | Zbl 0434.65085

5 J Cea, Approximation variationnelle des problèmes aux limites, Ann Inst Fourier,Vol 14, 1964, pp 345-444 | Numdam | MR 174846 | Zbl 0127.08003

6 P G Ciarlet, Quelques méthodes d'éléments finis pour le problème d'une plaque encastrée, Colloque I R I A sur « Méthodes de calcul scientifique et technique », Roquencourt, Pans, 17-21 décembre 1973, Springer-Verlag, Berlin, 1974 | MR 440954 | Zbl 0285.65042

7 P G Ciarlet, The Finite Element Method for Elliptic Problems, North Holland Publishing Co Amsterdam 1978 | MR 520174 | Zbl 0383.65058

8 P G Ciarlet and P A Raviart, General Lagrange and Hermite Interpolation in Rn with Applications to Finite Element Methods, Arch Rath Mech Anal, Vol 46, 1972, pp 177-199 | MR 336957 | Zbl 0243.41004

9 P G Ciarlet and P A Raviart, A Mixed Finite Element Method for the Biharmonic Equation, Symposium on Mathematical Aspects of Finite Elements m Partial Differential Equations, C DE BOOR, Éd , Academic Press, New York, 1974, pp 125-145 | MR 657977 | Zbl 0337.65058

10 G Fichera, Linear Elliptic Differential Systems and Eigenvalue Problems, Lectur Notes, Springer-Verlag, Berlin, 1965 | MR 209639 | Zbl 0138.36104

11 M Fortin, An Analysis of the Convergence of Mixed Finite Element Methods, R A I R O , Numer Anal, Vol 11, No 4, 1977, pp 341-354 | Numdam | MR 464543 | Zbl 0373.65055

12 C Johnson, On the Convergence of a Mixed Finite Element Method for Plate Bending Problems, Numer Math , Vol 21, 1973, pp 43-62 | MR 388807 | Zbl 0264.65070

13 C Johnson, Convergence of Another Mixed Finite Element Method for Plate Bending Problems, Report No 27, Department of Mathematics, Chalmers Institute of Technology and the University of Goteborg, 1972

14 J L Lions and E Magenes, Problèmes aux limites non homogènes et applications, Vol 1, Travaux Recherches Math , No 17, Dunod, Pans, 1968 | MR 247243 | Zbl 0165.10801

15 T Mjyoshi, Finite Element Method for the Solution of Fourth Order Partial Differential Equations, Kunamoto J Sc Math , Vol 9, 1973, pp 87-116

16 P A Raviart, Méthode des éléments finis, Cours 1972-1973 à l'Université de Pans VI

17 R Scholz, A Mixed Method for 4th Order Problems Using Linear Finite Elements, R A I R O , Numer Anal , Vol 12, No 1, 1978, pp 85-90 | Numdam | MR 483557 | Zbl 0382.65059

18 G Strang and G Fix, An Analysis of the Finite Element Method, Prentice Hall Englewood Cliffs, 1973 | MR 443377 | Zbl 0356.65096

19 S Timoschenko, Theory of Plates and Shells, McGraw-Hill, New York, 1959 | JFM 66.1049.02