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Numerical analysis of the general biharmonic problem by the finite element method. (English) Zbl 0541.65072

This paper deals with the solution of the biharmonic problem with mixed boundary conditions using curved triangular finite \(C^ 1\) elements and Bell’s elements. Error bounds in the \(L_ 2\) norm are found and the effects of numerical integration investigated.
Reviewer: J.D.P.Donnelly

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
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
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References:

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