Wang, Ming; Shi, Zhongci; Xu, Jinchao Some \(n\)-rectangle nonconforming elements for fourth order elliptic equations. (English) Zbl 1142.65451 J. Comput. Math. 25, No. 4, 408-420 (2007). 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. Cited in 33 Documents 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 Keywords:nonconforming finite element; fourth order elliptic equation; convergence PDFBibTeX XMLCite \textit{M. Wang} et al., J. Comput. Math. 25, No. 4, 408--420 (2007; Zbl 1142.65451)