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Some \(n\)-rectangle nonconforming elements for fourth order elliptic equations. (English) Zbl 1142.65451

Summary: Three \(n\)-rectangle nonconforming elements are proposed with \(n \geq 3\). They are the extensions of well-known Morley element, Adini element and Bogner-Fox-Schmit element in two spatial dimensions to any higher dimensions respectively. These elements are all proved to be convergent for a model biharmonic equation in \(n\) dimensions.

MSC:

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