\(C^{0}\)-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth-order elliptic problem

DOI10.1007/s00211-012-0508-2zbMath1276.65078OpenAlexW2068879743WikidataQ57653366 ScholiaQ57653366MaRDI QIDQ1950442

Hongru Chen, Shao-Chun Chen, ZhongHua Qiao

Publication date: 13 May 2013

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-012-0508-2

zbMATH Keywords

finite element methodfourth-order elliptic problembubble functionconsistence error\(C^{0}\)-nonconforming elementsfirst- and second-order convergence

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) Higher-order elliptic equations (35J30)

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Cites Work

• A discrete de Rham complex with enhanced smoothness
• A new class of Zienkiewicz-type non-conforming element in any dimensions
• Anisotropic conforming rectangular elements for elliptic problems of any order
• Polynomial approximation on tetrahedrons in the finite element method
• Vibration analysis of Kirchhoff plates by the Morley element method
• The Morley element for fourth order elliptic equations in any dimensions
• A robust nonconforming $H^2$-element
• Nonconforming tetrahedral finite elements for fourth order elliptic equations
• The F-E-M-Test for Convergence of Nonconforming Finite Elements
• The Generalized Patch Test
• Variational principles and the patch test
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• The Mathematical Theory of Finite Element Methods
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