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Sur une méthode d’éléments finis mixte pour l’équation biharmonique. (French) Zbl 0372.65039

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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References:
[1] 1. J. F. BOURGAT, Numerical study of a dual iterative method for solving a finite element approximation of the biharmonic equation, Computer Methods in Apliey Mechanics and Engineering, 9, 1976, p. 203-218. Zbl0335.65052 MR431743 · Zbl 0335.65052 · doi:10.1016/0045-7825(76)90062-1
[2] 2. F. BREZZI and P. A. RAVIART, Mixed finite element methods for 4th order elliptic equations, École Polytechnique, Rapport Interne No 9, mai 1976. Zbl0434.65085 MR657975 · Zbl 0434.65085
[3] 3. P. G. CIARLET, Numerical Analysis of the Finite Element Method, Séminaires de Mathématiques Supérieures, Presses de l’Université de Montréal, 1975. Zbl0363.65083 MR495010 · Zbl 0363.65083
[4] 4. P. G. CIARLET and R. GLOWINSKI, Dual iterative techniques for solving a finite element approximation of the biharmonic equation, Computer Methods in Applied Mechanics and Engineering, 5, 1975, p. 277-295. Zbl0305.65068 MR373321 · Zbl 0305.65068 · doi:10.1016/0045-7825(75)90002-X
[5] 5. P. G. CIARLET, P. A. RAVIART, Interpolation theory over curved elements with applications to finite element methods, Computer Methods in Applied Mechanics and Engineering, 1, 1972, p. 217-249. Zbl0261.65079 MR375801 · Zbl 0261.65079 · doi:10.1016/0045-7825(72)90006-0
[6] 6. P. G. CIARLET, P. A. RAVIART, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, 409-474, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Ey. A. K. Aziz., Acayemic Press, 1972. Zbl0262.65070 MR421108 · Zbl 0262.65070
[7] 7. P. G. CIARLET, P. A. RAVIART, A mixed finite element method for the biharmonic equation, 125-145, Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, 1974. Zbl0337.65058 MR657977 · Zbl 0337.65058
[8] 8. J. NE_AS, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris, 1967. · Zbl 1225.35003
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