On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation

DOI10.1007/s00211-004-0536-7zbMath1065.65135OpenAlexW2012929744MaRDI QIDQ704805

Shangyou Zhang

Publication date: 19 January 2005

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

Full work available at URL: https://doi.org/10.1007/s00211-004-0536-7

zbMATH Keywords

numerical examplesfinite element methodselliptic equationsmesh refinementpiecewise constant approximations for Jacobiansquadrilateral and hexahedral elements

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (8)

Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements ⋮ Accurate numerical integration for the quadrilateral and hexahedral finite elements ⋮ Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions ⋮ Optimal quadrilateral finite elements on polygonal domains ⋮ Lowest-order weak Galerkin finite element methods for linear elasticity on rectangular and brick meshes ⋮ Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes ⋮ A stabilizer free weak Galerkin finite element method on polytopal mesh. III ⋮ A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials

Cites Work

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• Quadrilateral mesh
• A convergence condition for the quadrilateral Wilson element
• Analytical integral formulae related to convex quadrilateral finite elements
• The reference coordinates and disortion measures for quadrilateral hybrid stress membrane element
• Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements
• Superconvergence in Galerkin finite element methods
• Some geometrical results and estimates for quadrilateral finite elements
• Further results for enhanced strain methods with isoparametric elements
• Some analytical integration formulae for a four node isoparametric element
• Superconvergence and Reduced Integration in the Finite Element Method
• Estimation of the Interpolation Error for Quadrilateral Finite Elements Which Can Degenerate into Triangles
• Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
• Approximation by quadrilateral finite elements
• A Stable Affine-Approximate Finite Element Method
• A Local Projection Operator for Quadrilateral Finite Elements
• Some pre-computed universal numeric arrays for linear convex quadrilateral finite elements

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