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An equilibrium finite element method for fourth order elliptic equations with variable coefficients. (English) Zbl 0697.65082
The present work is devoted to the fourth order Dirichlet problem with variable or constant coefficients on a convex polygon. It follows the lines developed by Fraeijs de Veubeke with regard to the equilibrium finite element method. For bending problems of plates, the method thus developed gives a simultaneous approximation to displacement and bending and twisting moment tensor.
The paper includes a result stating that a certain space of functionals, which is known to be unisolvent with respect to the space of symmetric polynomials of degree less or equal than 3, is not unisolvent when the degree is greater or equal than 6, leaving thus open the question with respect to degrees 4 and 5. The closing sections deal with error estimates for the equilibrium finite element solution and illustrative examples of the method.
Reviewer: J.P.Milaszewicz

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
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