Error estimates for mixed methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 14 (1980) no. 3, p. 249-277
@article{M2AN_1980__14_3_249_0,
     author = {Falk, Richard S. and Osborn, J. E.},
     title = {Error estimates for mixed methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {14},
     number = {3},
     year = {1980},
     pages = {249-277},
     zbl = {0467.65062},
     mrnumber = {592753},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1980__14_3_249_0}
}
Falk, R. S.; Osborn, J. E. Error estimates for mixed methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 14 (1980) no. 3, pp. 249-277. http://www.numdam.org/item/M2AN_1980__14_3_249_0/

1 I. Babu Ka, Error-Bounds for Finite Element Method, Numer Math , Vol. 16, 1971, pp. 322-333. | MR 288971 | Zbl 0214.42001

2 I. Babu Ka and A. Aziz, Survey Lectures on the Mathematical Foundations of the Finite Element Method in The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations, A. K. Aziz, Ed, Academic Press, New York, 1973, pp. 5-359. | Zbl 0268.65052

3 I. Babu Ka, J. Osborn and J. Pitkaranta , Analysis of Mixed Methods for 4th Order Elliptic Equations (to appear).

4 J. Bramble and S. Hilbert, Estimation of Linear Functionals on Sobolov Spaces with Application to Fourier Transforms and Spline Interpolation, S.I. A. M . J. Numer Anal, Vol .13, 1976, pp. 185-197. | Zbl 0201.07803

5 F. Brezzi, On theExistence, Uniqueness and Approximation of Saddle-Point Problems Ansing from Lagrangian Multipliers, R. A. I. R. O. , Vol. 8 R2, 1974, pp 129-151. | Numdam | MR 365287 | Zbl 0338.90047

6 F. Brezzi, Sur la méthode des éléments finis hybrides pour le problème biharmonique, Numer. Math., Vol. 24, 1975, pp 103-131. | MR 391538 | Zbl 0316.65029

7 F. Brezzi and P. Raviart, Mixed Finite Element Methods for 4th Ordej Elliptic Equations, Topics inNumencal Analysis III, J. MILLER, Ed , Academic Press, 1978. | Zbl 0434.65085

8 P. Giarlet, The Finite Element Method for Elliptic Problems, North-Holland, 1978. | MR 520174 | Zbl 0383.65058

.9 P. Ciarlet and P. Raviart, A Mixed Finite Element Method for the Biharmonic Equation, Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, C. DE BOOR, Ed., Academic Press, New York, 1974, pp. 125-143. | MR 657977 | Zbl 0337.65058

10 M. Crouzeix and P. Raviart, Conforming and Nonconforming Finite Element Methods for Solving the Stationary Stokes Equations I, R. A. I. R. O. , Vol. R-3, 1973, pp 33-76. | Numdam | MR 343661 | Zbl 0302.65087

11 M. Fortin, Analysis of the Convergence of Mixed Finite Element Methods, R.A.I.R.O.,Vol. 11, 1977, pp. 341-354. | Numdam | MR 464543 | Zbl 0373.65055

12 R. Glowinski, Approximations externes, par elements finis deLagrange d'ordre un et deux, du probleme de Dinchlet pour l'operateur biharmonique Methodes iteratives de resolution des problemes approches In Topics in Numencal Analysis, J.J. .H MILLER, Ed., Academic Press, New York, 1973, pp. 123-171. | MR 351120 | Zbl 0277.35003

13 P. Grisvard, Singular Solutions of Elliptic Boundary Value Problems, Lecture Notes,University of Maryland (to appear). | Zbl 0567.35025

14 L. Herrmann, Finite Element Bending Analysis for Plates, J. Eng Mech Div A. S.C. E. E. M5, Vol. 93, 1967, pp. 49-83.

15 L. Herrmann, A Bending Analysis for Plates, Proc. Conf. On Matrix Methods in Structural Mechanics, AFFDL-TR-66-68, pp. 577-604.

16 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

17 R. Kellogg and J. Osborn, A regularity Result for the Stokes Problem, J Funct Anal., Vol. 21, 1976, pp. 397-431. | MR 404849 | Zbl 0317.35037

18 B. Mercier, Numerical Solution of the Biharmonic Problem by Mixed Finite Elements of Class C, Bull. Un. Mat. Ital. , Vol. 10, 1974, pp. 133-149. | MR 378442 | Zbl 0332.65058

19 T. Miyoshi, Finite Element Method for the Solution of Fourth Order Partial Differential Equations, Kunamoto J. Sc. (Math.), Vol. 9, 1973, pp. 87-116. | MR 386298 | Zbl 0249.35007

20 J. Oden, Some Contributions to the Mathematical Theory of Mixed Finite Element Approximations In Theory and Practice in Finite Element Structural Analysis, University of Tokyo Press, 1973, pp. 3-23. | Zbl 0374.65060

21 R. Rannacher, On Nonconforming and Mixed Finite Element Methods for Plate Bending Problems The Linear Case, R. A. I. R. O. , Vol. 13, 1979, pp. 369-387. | Numdam | MR 555385 | Zbl 0425.35042

22 P. Raviart and J. Thomas, A Mixed Finite Element Method for 2nd Order Elliptic Problems, Lecture Notes in math , No 606, Berlin-Heidelberg-New York, Springer, 1977, pp. 292-315. | MR 483555 | Zbl 0362.65089

23 R. Scholz, Approximation von Sattelpunkten mit finiten Elementen, Tagungsband, Bonn. Math. Schr., Vol.. 89, 1976, pp. 53-66. | MR 471377 | Zbl 0359.65096

24 R. Scholz, A Mixed Method for 4th Order Problems using Linear Finite Elements, R. A. I. R. O. , Vol. 12, 1978, pp. 85-90. | Numdam | MR 483557 | Zbl 0382.65059

25 J. Thomas, Sur l'Analyse numérique des méthodes d'élements finis hybrides et mixtes, Thesis, Pierre-et-Marie-Curie, Paris, 1977.