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A mixed method for 4th order problems using linear finite elements. (English) Zbl 0382.65059

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
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[1] 1. F. BREZZI and P. A. RAVIART, Mixed Finite Element Methods for Mh Order Elliptic Equations (to appear). Zbl0434.65085 · Zbl 0434.65085
[2] 2. P. G. CIARLET and P. A. RAVIART, Interpolation Theory Over Curved Elements, with Applications to Finite Element Methods, Computer Meth. Appl. Mech. Engrg., 1, 1972, pp. 217-249. Zbl0261.65079 MR375801 · Zbl 0261.65079 · doi:10.1016/0045-7825(72)90006-0
[3] 3. P. G. CIARLET and P. A. RAVIART, A Mixed Finite Element Method for the Biharmonic Equation in Mathematical Aspects of Finite Elements in Partial Differential Equations, C. DEBOOR, Ed., Proc. Symp. Math. Res. Center, Univ. Wisconsin, April 1-3, 1974, Academic Press, New York - San Francisco- London, 1974, pp. 125-145. Zbl0337.65058 MR657977 · Zbl 0337.65058
[4] 4. J. FREHSE and R. RANNACHER, Eine \(L^1\)-Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente, Bonner Math. Schriften, 89, 1976, pp. 92-114. Zbl0359.65093 MR471370 · Zbl 0359.65093
[5] 5. S. G. MDCHLIN, The Problem of the Minimum of a Quadratic Functional, Holden-Day, Inc., San Francisco - London - Amsterdam, 1965. Zbl0121.32801 MR171196 · Zbl 0121.32801
[6] 6. J. NITSCHE, \(L_\infty\)-Convergence of Finite Element Approximations, Rom, 1975 (to appear). Zbl0362.65088 MR568857 · Zbl 0362.65088
[7] 7. J. NITSCHE, \(L_infty\)-convergence of the Ritz-method with linear finite elements for second order elliptic boundary value problems (to appear in the anniversary volume dedicated to academician I. N. Vekua). Zbl0424.35033 MR513396 · Zbl 0424.35033
[8] 8. R. RANNACHER, Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem, Manuscripta Math., 19, 1976, pp. 401-416. Zbl0383.65061 MR423841 · Zbl 0383.65061 · doi:10.1007/BF01278927 · eudml:154424
[9] 9. R. SCHOLZ, Approximation von Sattelpunkten mit finiten Elementen, Bonner Math. Schriften, 89, 1976, pp. 53-66. Zbl0359.65096 MR471377 · Zbl 0359.65096
[10] 10. M. ZLAMAL, Curved Elements in the Finite Element Method, I. S.LA.M. J. Numer. Anal., 10, 1973, pp. 229-240; II. S.I.A.M. J. Numer. Anal.,11, 1974, pp. 347-362. Zbl0285.65067 MR395263 · Zbl 0285.65067 · doi:10.1137/0710022
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