Geodesic
A family of C 1 finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 13 (1979) no. 3, pp. 227-255.

Voir la notice de l'article provenant de la source Numdam

@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 = {ESAIM: Mathematical Modelling and Numerical Analysis },
     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://geodesic.mathdoc.fr/item/M2AN_1979__13_3_227_0/}
}
TY  - JOUR
AU  - Douglas, Jim Jr.
AU  - Dupont, Todd
AU  - Percell, Peter
AU  - Scott, Ridgway
TI  - A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 1979
SP  - 227
EP  - 255
VL  - 13
IS  - 3
PB  - Centrale des revues, Dunod-Gauthier-Villars
PP  - Montreuil
UR  - http://geodesic.mathdoc.fr/item/M2AN_1979__13_3_227_0/
LA  - en
ID  - M2AN_1979__13_3_227_0
ER  - 
%0 Journal Article
%A Douglas, Jim Jr.
%A Dupont, Todd
%A Percell, Peter
%A Scott, Ridgway
%T A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 1979
%P 227-255
%V 13
%N 3
%I Centrale des revues, Dunod-Gauthier-Villars
%C Montreuil
%U http://geodesic.mathdoc.fr/item/M2AN_1979__13_3_227_0/
%G en
%F M2AN_1979__13_3_227_0
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. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 13 (1979) no. 3, pp. 227-255. http://geodesic.mathdoc.fr/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. | Zbl | MR

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

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

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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

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

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. | Zbl | MR

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. | Zbl | MR | mathdoc-id

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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

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. | Zbl | MR

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. | Zbl | MR

23. J. Morgan and R. Scott, A nodal basis for C 1 piecewise polynomials of degree n≥5, Math. Comp., Vol. 29, 1975, pp. 736-740. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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

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

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. | Zbl | MR

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