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The Morley element for fourth order elliptic equations in any dimensions. (English) Zbl 1092.65103
The authors introduce a new \(n\)-dimensional \((n>2)\) Morley finite element and carry out a fairly complete analysis. They give an explicit construction of the nodal basis functions and discuss some basic properties. When finite element spaces corresponding to these elements are used, in order to solve the classical boundary value problem for the biharmonic equation, a convergence result is eventually proved.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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