The local superconvergence of the linear finite element method for the poisson problem

DOI10.1002/num.21842zbMath1297.65133OpenAlexW2155685275MaRDI QIDQ5418784

Zhongliang Wen, Qiding Zhu, Jun-Zhi Cui, Wen-ming He

Publication date: 28 May 2014

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21842

zbMATH Keywords

Green's functionRichardson extrapolationPoisson problemdisplacementlocal superconvergencelinear finite element methodtensor-product block

Mathematics Subject Classification ID

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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (2)

Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients ⋮ The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain

Cites Work

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• Generalized Rayleigh quotient and finite element two-grid discretization schemes
• Asymptotic error expansion and Richardson extrapolation for linear finite elements
• Asymptotic expansions and \(L^{\infty}\)-error estimates for mixed finite element methods for second order elliptic problems
• Superconvergence in Galerkin finite element methods
• A new superconvergence and extrapolation for second order triangular element
• Pointwise Error Estimates and Asymptotic Error Expansion Inequalities for the Finite Element Method on Irregular Grids: Part II. Interior Estimates
• Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids
• A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
• Superconvergence of interpolated collocation solutions for Hammerstein equations
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• Pointwise supercloseness of tensor‐product block finite elements
• Weighted Sobolev Spaces and Degenerate Elliptic Equations
• ISOLATION OF SINGULARITIES OF THE GREEN'S FUNCTION

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