zbMATH — the first resource for mathematics

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
Full Text: DOI EuDML
[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 · eudml:193267
[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 · eudml:154424
[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 · eudml:132626
[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 · eudml:193314
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.