A family of 3D \(H^2\)-nonconforming tetrahedral finite elements for the biharmonic equation

DOI10.1007/s11425-019-1661-8zbMath1446.65171arXiv1909.08178OpenAlexW3025039413WikidataQ114222419 ScholiaQ114222419MaRDI QIDQ2193951

Shangyou Zhang, Jun Hu, Shudan Tian

Publication date: 25 August 2020

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

Full work available at URL: https://arxiv.org/abs/1909.08178

zbMATH Keywords

finite element methodbiharmonic problemtetrahedral grid\(H^2\)-nonconforming element

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (9)

A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids ⋮ A fast Fourier-Galerkin method solving a system of integral equations for the biharmonic equation ⋮ Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems ⋮ A family of H-div-div mixed triangular finite elements for the biharmonic equation ⋮ Construction and analysis of the quadratic finite volume methods on tetrahedral meshes ⋮ High accuracy nonconforming biharmonic element over n‐rectangular meshes ⋮ Four-order superconvergent CDG finite elements for the biharmonic equation on triangular meshes ⋮ A Conforming Dg Method for the Biharmonic Equation on Polytopal Meshes ⋮ An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new a priori error estimate of nonconforming finite element methods
• A family of non-conforming elements and the analysis of Nitsche's method for a singularly perturbed fourth order problem
• A new class of Zienkiewicz-type non-conforming element in any dimensions
• A family of 3D continuously differentiable finite elements on tetrahedral grids
• High accuracy nonconforming finite elements for fourth-order problems
• \(C^{0}\)-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth-order elliptic problem
• A Note on the Nonconforming Finite Elements for Elliptic Problems
• The Lowest Order Differentiable Finite Element on Rectangular Grids
• Variational principles and the patch test
• Minimal finite element spaces for $2m$-th-order partial differential equations in $R^n$
• On the Full C₁-Q_k Finite Element Spaces on Rectangles and Cuboids
• The Quadratic Specht Triangle
• The Mathematical Theory of Finite Element Methods
• The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids

This page was built for publication: A family of 3D \(H^2\)-nonconforming tetrahedral finite elements for the biharmonic equation