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A potential method for the biharmonic equation. (English) Zbl 0527.65075


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
74S05 Finite element methods applied to problems in solid mechanics
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
74K20 Plates
76B47 Vortex flows for incompressible inviscid fluids
35J40 Boundary value problems for higher-order elliptic equations
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References:

[1] Amara, M., Destuynder, P.: A Numerical Method for the Biharmonic Problem, Rapport Interne No. 63, Ecole Polytechnique. Palaiseau, France 1981 · Zbl 0476.73061
[2] Brebbia, C.A., Walker, S.: Boundary Element Techniques in Engineering. London: Newnes-Butterworths 1980 · Zbl 0444.73065
[3] Brezzi, F., Raviart, P.A.: Mixed Finite Element Methods for Fourth Order Elliptic Equations. Rapport Interne No. 9, Ecole Polytechnique, Palaiseau, France 1976 · Zbl 0434.65085
[4] Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland 1978 · Zbl 0383.65058
[5] Ciarlet, P.G., Glowinski, R.: Dual Iterative Techniques for solving a Finite Element Approximation of the Biharmonic Equation. Comput. Methods Appl. Mech. Engrg.5, 277-295 (1975) · Zbl 0305.65068
[6] Ciarlet, P.G., Raviart, P.A.: A Mixed Finite Element Method for the Biharmonic Equation. In: Mathematical Aspects of Finite Elements in Partial Differential Equations. Boor, de, C. (ed.). New York: Academic Press, pp. 125-145, 1974 · Zbl 0337.65058
[7] Glowinski, R., Pironneau, O.: Numerical Methods for the First Biharmonic Equation and for the Two-Dimensional Stokes Problem. Report No. STAN-CS-77-615, Computer Science Department, Stanford University, USA 1977 · Zbl 0365.65072
[8] Jaswon, M.A., Symm, G.T.: Integral Equation Methods in Potential Theory and Elastostatics. New York: Academic Press 1977 · Zbl 0414.45001
[9] Kondrat’ev, V.A.: Boundary Value Problems for Elliptic Equations in Domains with Conical or Angular Points. Trudy Markov. Mat. Obsc. Vol.16, 209-292 (1967)
[10] Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0227.35001
[11] Mikhlin, S.G.: Mathematical Physics, An Advanced Course. Amsterdam: North-Holland 1970 · Zbl 0202.36901
[12] Osborn, J.E.: Regularity of Solutions of the Stokes’ Problem in a Polygonal Domain. In: Numerical Solution of Partial Differential Equations-111, Synspade 1975. Hubbard, B. (ed.). New York: Academic Press 1976
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