Internal finite element approximation in the dual variational method for the biharmonic problem. (English) Zbl 0584.65068

The paper presents a conforming finite element method for the dual variational formulation of the biharmonic problem with mixed boundary conditions. This allows \(C^ 0\)-elements to be used when the primal problem requires \(C^ 1\)-elements. The solution yields the second derivatives of the solution. The method depends on the existence of a vector potential for the equilibrium bending moment.
Reviewer: J.D.P.Donnelly


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.)
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J40 Boundary value problems for higher-order elliptic equations
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