A family of C 1 finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
RAIRO. Analyse numérique, Tome 13 (1979) no. 3, pp. 227-255.
@article{M2AN_1979__13_3_227_0,
     author = {Douglas, Jim Jr. and Dupont, Todd and Percell, Peter and Scott, Ridgway},
     title = {A family of $C^1$ finite elements with optimal approximation properties for various {Galerkin} methods for 2nd and 4th order problems},
     journal = {RAIRO. Analyse num\'erique},
     pages = {227--255},
     publisher = {Centrale des revues, Dunod-Gauthier-Villars},
     address = {Montreuil},
     volume = {13},
     number = {3},
     year = {1979},
     mrnumber = {543934},
     zbl = {0419.65068},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1979__13_3_227_0/}
}
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Douglas, Jim Jr.; Dupont, Todd; Percell, Peter; Scott, Ridgway. A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems. RAIRO. Analyse numérique, Tome 13 (1979) no. 3, pp. 227-255. http://www.numdam.org/item/M2AN_1979__13_3_227_0/

1. S. Gmon, Elliptic Boundary Values Problems, D. van Nostrand, 1965.

2. A. Berger, R. Scott and G. Strang, Approximate Boundary Conditions in the Finite Element Method, Symposia Mathematica, X, Academic Press, 1972, pp. 295-313. | MR | Zbl

3. S. Bergman and M. Schiffer, Kernel Functions and Elliptic Differential Equations in Mathematical Physics, Academic Press, 1953. | MR | Zbl

4. J. J. Blair, Higher Order Approximations to the Boundary Conditions for the Finite element Method, Math. Comp., Vol. 30, 1976, pp. 250-262. | MR | Zbl

5. J. H. Bramble and S. R. 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 | Zbl

6. J. H. Bramble and A. H. Schatz, Rayleigh-Ritz-Galerkin Methods for Dirichlet's Problem Using Subspaces Without Boundary Conditions, Comm. Pure App. Math.,Vol. 23, 1970, pp. 653-674. | MR | Zbl

7. J. H. Bramble and A. H. Schatz, Least Squares Methods for 2m-th Order Elliptic Boundary-Value Problems, Math. Comp., Vol. 25, 1971, pp. 1-32. | MR | Zbl

8. P. G. Ciarlet, Sur l'élément de Clough et Tocher, R.A.I.R.O., Analyse numérique, Vol. 2, 1974, pp. 19-27. | Numdam | MR | Zbl

9. P. G. Ciarlet, Numerical Analysis of the Finite Element Method, Séminaire de Mathématiques supérieures, Université de Montréal, 1975. | MR | Zbl

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

11. J. F. Ciavaldini and J. C. Nedelec, Sur l'élement de Fraeijs de Veubeke et Sander, R.A.I.R.O., Analyse numérique, Vol. 2, 1974, pp. 29-46. | Numdam | MR | Zbl

12. R. W. Clough and J. L. Tocher, Finite Element Stiffness Matrices and Analysis of Plates in Bending, Proceedings of Conference on Matrix Methods in Structural Mechanics, Wright-Patterson AFB, 1965.

13. J. Jr. Douglas, H1-Galerkin Methods for a Nonlinear Dirichlet Problem, Mathematical Aspects of Finite Element Methods, Rome, 1975, Lecture Notes in Mathematics, n° 606, Springer-Verlag, 1977, pp. 64-86. | MR | Zbl

14. J. Jr. Douglas and T. Dupont, Collocation Methods for Parabolic Equations in a Single Space Variable, Lecture Notes in Mathematics, n° 385, Springler-Verlag, 1974. | MR | Zbl

15. J. Jr. Douglas and T. Dupont, H~1-Galerkin Methods for Problems Involving Several space Variables, Topics in Numerical Analysis, III, John J. H. MILLER, éd., Academic Press, 1977, pp. 125-141. | MR | Zbl

16. J. Jr. Douglas, T. Dupont and M. F. Wheeler, H1-Galerkin Methods for the Laplace and Heat Equations, Mathematical Aspects of Finite Elements in Partial Differential Equations, C. DEBOOR, éd., Academic Press, 1974, pp. 383-416. | MR | Zbl

17. T. Dupont and R. Scott, Polynomial Approximation of Functions in Sobolev Spaces, submitted Math. Comp. | MR | Zbl

18. B. Fraeijs Deveubeke, Bending and Stretching of Plates, Proceedings of Conference on Matrix Methods in Structural Mechanics, Wright-Patterson AFB, 1965.

19. P. Grisvard, Behavior of the Solutions of an Elliptic Boundary Value Problem in Polygonal or Polyhedral Domain, Numerical Solution of Partial Differential Equations, III (Synspade, 1975), Bert HUBBARD, éd., Academic Press, 1976,pp.207-274. | MR | Zbl

20. P. Jamet, Estimation de Verreur d'interpolation dans un domaine variable et application aux éléments finis quadrilatéraux dégénérés, in Méthodes numériques enmathématiques appliquées (Séminaire de Mathématiques supérieures, été 1975),Presses de l'Université de Montréal, Vol. 60, 1977. | Zbl

21. I. N. Katz, A. G. Peano and B. A. Szabo, Nodal Variables for Arbitrary Order Conforming Finite Eléments, U. S. Dept. of Transportation Tech. Rep. DOT-OS-30108-5, Washington Univ., June, 1975.

22. J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, 1968. | MR | Zbl

23. J. Morgan and R. Scott, A nodal basis for C 1 piecewise polynomials of degree n5, Math. Comp., Vol. 29, 1975, pp. 736-740. | MR | Zbl

24. J. Nitsche, On Dirichlet Problems Usina Subspaces with Nearly Zero Boundary Conditions, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz, éd., Academic Press, 1972, pp. 603-628. | MR | Zbl

25. A.G. Peano, Hierarchies of Conforming Finite Elements for Plane Elasticity and Plate Bending, Comp. and Maths, with Appls., VoL 2, 1976t pp. 211-224. | Zbl

26. P. Percell, On Cubic and Quartic Clough-Tocher Finite Eléments, S.I.A.M.J. Numer. Anal., Vol. 13, 1976, pp. 100-103. | MR | Zbl

27. G. Sander, Bornes supérieures et inférieures dans l'analyse matricielle des plaques en flexion-torsion, Bull. Soc. Royale des Se. de Liège, Vol. 33, 1964, pp, 456-494. | MR

28. A. H. Schatz, An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms, Math. Comp., Vol. 28, 1974, pp. 959-962. | MR | Zbl

29. R. Scott, C1 Continuity via Constraints for 4th Order Problems, Mathematical Aspects of Finite Eléments in Partial Differential Equations, C. DEBOOR, éd., Academic Press; 1974, pp. 171-193. | MR | Zbl

30. R. Scott, Interpolatetl Boundarv Conditions in the Finite Element Method, S.LA.M.J. Numer. Anal., Vol. 12, 1975, pp. 404-427. | MR | Zbl

31. G. Strang, Piecewise Polynomials and the Finite Element Method, Bull. A.M.S.,VoL 79, 1973, pp. 1128-1137. | MR | Zbl

32. B.A. Szabo et al., Advanced Design Technology for Rail Transportation Vehicles, .S.Dept. of Transportation Tech. Rep. DOT-OS-30108-2, Washington Univ., June, 1974.

33. V. Thomée and L. Wahlbin, On Galerkin Methods in Semi-Linear Parabolie Problems, S.I.A.M. J. Num. Anal., VoL 12, 1975, pp. 378-389. | MR | Zbl

34. O. C. Zienkiewicz, TheFinite Element Method in Engineering Science, McGraw-Hill, 1971. | MR | Zbl