On nonconforming and mixed finite element methods for plate bending problems. The linear case. (English) Zbl 0425.35042


35J40 Boundary value problems for higher-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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[1] 1. F. BREZZI and P. A. RAVIART, Mixed Finite Element Methodsfor 4th Order Ellipticquations In Topics inNumerical Analysis, Vol.III, J. J. H. MILLER, Ed., Academic Press, 1978. Zbl0434.65085 · Zbl 0434.65085
[2] 2. P. G. CIARLET, Conforming and Nonconforming Finite Element Methods for SolvingthePlate ProblemIn Numerical Solution of Differential Equations, G. A.WATSON, Ed., Springer, 1974. Zbl0285.65072 MR423832 · Zbl 0285.65072
[3] 3. P.G. CIARLET and P.A. RAVIART, A mixed Finite Element Method for the Biharmonic Equation In Mathematical Aspects of Finite Eléments in Partial Differential Equations, C. DEBOOR, Ed., Academic Press, 1974. Zbl0337.65058 · Zbl 0337.65058
[4] 4. P. LASCAUX and P. LESAINT, Some Nonconforming Finite Elements for the Plate Bending Problem, R.A.I.R.O., Anal. Nurnér., Vol. 1, 1975, pp. 9-53 Zbl0319.73042 MR423968 · Zbl 0319.73042
[5] 5. T. MIYOSHI, Finite Element Method for the Solution of A-th Order Partial Differential Equations, Kumamoto J. Sc.Math., Vol. 9, 1973, pp. 87-116. Zbl0249.35007 MR386298 · Zbl 0249.35007
[6] 6. J. A. NITSCHE, Convergence of Nonconforming Methods In Numerical Solution of Differential Equations, G. A. WATSON, Ed., Springer, 1974. Zbl0367.65064 MR658316 · Zbl 0367.65064
[7] 7. J. A.N NITSCHE, On Projection Methods for the Plate Problem In Numerical Analysis, J. DESCLOUX and J. MARTI, Ed., Birkhauser, 1977. Zbl0361.65097 MR468521 · Zbl 0361.65097
[8] 8. R. RANNACHER, Punktweise Konvergenz der Methode der finiten Elemente beimPlattenproblem, Manuscripta math., Vol. 19, 1976, pp. 401-416. Zbl0383.65061 MR423841 · Zbl 0383.65061 · doi:10.1007/BF01278927
[9] 9. R. RANNACHER, Finite Element Approximation of Simply Supported Plates and the Babuska Paradox, Z. Angew. Math. Mech., Vol. 59, 1979, pp. T 73-T 76 Zbl0421.73072 MR533989 · Zbl 0421.73072 · doi:10.1002/zamm.19790590202
[10] 10. R RANNACHER, Nonconforming Finite Element Methods for Eigenvalue Problems in Linear Plate Theory, Numer. Math., Vol. 32, 1979 (to appear). Zbl0394.65035 MR545740 · Zbl 0394.65035 · doi:10.1007/BF01396493
[11] 11. R. SCHOLZ, Approximation von Sattelpunkten mit finiten Elementen In Finite Elemente,Tagungsband, Bonn, Math. Schr., Vol. 89, 1976, pp. 53-66. Zbl0359.65096 MR471377 · Zbl 0359.65096
[12] 12. R. SCHOLZ, A Mixed Methodfor 4th Order Problems using Linear Finite Eléments, R.A.I.R.O., Anal. Numer., Vol. 12, 1978, pp. 85-90. Zbl0382.65059 MR483557 · Zbl 0382.65059
[13] 13. J. FREHSE and R. RANNACHER, Eine L 1 -Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente In Finite Elemente,Tagungsband, Bonn, Math.Schr., Vol. 89, 1976, pp. 92-114. Zbl0359.65093 MR471370 · Zbl 0359.65093
[14] 14. J. A. NITSCHE, L \infty -convergence of finite element approximations, Second Conference on Finite Eléments, Rennes, 1975. Zbl0362.65088 MR568857 · Zbl 0362.65088
[15] 15. R. SCOTTOptimal L \infty estimates for the finite element method on irregular meshes, Math. Comp., Vol. 30, 1976, pp. 681-697. Zbl0349.65060 MR436617 · Zbl 0349.65060 · doi:10.2307/2005390
[16] 16. R. B. KELLOGG and J. E. OSBORN, A Regularity Resuit for the Stokes Problem in aConvex Poligon. J. Funet. Anal., Vol. 21, 1976, pp.397-431. Zbl0317.35037 MR404849 · Zbl 0317.35037 · doi:10.1016/0022-1236(76)90035-5
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