\(\eta\%\)-superconvergence in the interior of locally refined meshes of quadrilaterals: Superconvergence of the gradient in finite element solutions of Laplace's and Poisson's equations

DOI10.1016/0168-9274(94)00029-8zbMath0823.65101OpenAlexW2049782910MaRDI QIDQ1344317

S. K. Gangaraj, Theofanis Strouboulis, Ivo M. Babuška, Chandra Shekhar Upadhyay

Publication date: 24 October 1995

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(94)00029-8

zbMATH Keywords

numerical examplesfinite elementsuperconvergencegradientLaplace equationPoisson equationcomputer based approach

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)

Related Items (11)

Validation of recipes for the recovery of stresses and derivatives by a computer-based approach ⋮ \(\eta\%\)-superconvergence in the interior of locally refined meshes of quadrilaterals: Superconvergence of the gradient in finite element solutions of Laplace's and Poisson's equations ⋮ Adaptive numerical solution of thick plates using first-order shear deformation theory. Part II: Adaptivity ⋮ \(\eta\%\)-Superconvergence of finite element approximations in the interior of general meshes of triangles ⋮ Pollution error in the \(h\)-version of the finite element method and the local quality of the recovered derivatives ⋮ Derivative superconvergence of rectangular finite elements for the Reissner-Mindlin plate ⋮ Recovery-based error estimators for the VEM and BEM-based FEM ⋮ 2D and 3D finite element meshing and remeshing ⋮ Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis ⋮ Superconvergence results on mildly structured triangulations ⋮ Unnamed Item

Cites Work

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• On superconvergence techniques
• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
• A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
• Asymptotically exact a posteriori error estimator for biquadratic elements
• Analysis of mixed finite element methods on locally refined grids
• Recent experiences with error estimation and adaptivity. II: Error estimation for \(h\)-adaptive approximations on grids of triangles and quadrilaterals
• Validation of recipes for the recovery of stresses and derivatives by a computer-based approach
• \(\eta\%\)-superconvergence in the interior of locally refined meshes of quadrilaterals: Superconvergence of the gradient in finite element solutions of Laplace's and Poisson's equations
• Pollution-error in the \(h\)-version of the finite-element method and the local quality of a posteriori error estimators
• \(\eta\%\)-Superconvergence of finite element approximations in the interior of general meshes of triangles
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 2, Refinements
• Superconvergence and Reduced Integration in the Finite Element Method
• Some mesh schemes for quasi-linear elliptic equations
• Asymptotically Exact Error Estimators for Rectangular Finite Elements
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• Interior Estimates for Ritz-Galerkin Methods
• Maximum-Norm Interior Estimates for Ritz-Galerkin Methods
• Interior Maximum Norm Estimates for Finite Element Methods
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 1
• Superconvergence of the gradient of finite element solutions
• Performance of the h–p version of the finite element method with various elements
• Superconvergence of the gradient of Galerkin approximations for elliptic problems

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