High accuracy nonconforming finite elements for fourth-order problems

DOI10.1007/s11425-012-4429-4zbMath1264.65200OpenAlexW2269549780MaRDI QIDQ1933998

PengHe Zu, Ming Wang, Shuo Zhang

Publication date: 28 January 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4429-4

zbMATH Keywords

convergencenumerical exampleshigh accuracynonconforming finite elementarbitrary dimensionfourth-order problem

Mathematics Subject Classification ID

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

Related Items (7)

Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions ⋮ A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids ⋮ Capacity of the Adini element for biharmonic equations ⋮ High accuracy nonconforming biharmonic element over n‐rectangular meshes ⋮ A family of 3D \(H^2\)-nonconforming tetrahedral finite elements for the biharmonic equation ⋮ Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems ⋮ An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations

Cites Work

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• A new class of Zienkiewicz-type non-conforming element in any dimensions
• Polynomial approximation on tetrahedrons in the finite element method
• The Morley element for fourth order elliptic equations in any dimensions
• On the Necessity and Sufficiency of the Patch Test for Convergence of Nonconforming Finite Elements
• A Note on the Nonconforming Finite Elements for Elliptic Problems
• Nonconforming tetrahedral finite elements for fourth order elliptic equations
• The Generalized Patch Test
• Variational principles and the patch test

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