\(\eta\%\)-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
type: Item
instance of: scholarly article
title: \(\eta\%\)-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
zbMATH Open document ID: 0823.65101
DOI: 10.1016/0168-9274(94)00029-8
author: S. K. Gangaraj
author: Ivo Babuška
author: Theofanis Strouboulis
author: C. S. Upadhyay
published in: Applied Numerical Mathematics
publication date: 1995-10-24T00:00:00Z
review text: The paper deals with the concept of \(\eta\%\)-superconvergence of finite element solutions. A point of \(\eta\%\)-superconvergence is a point where the approximation error, in the limit when refining the mesh, does not exceed \(\eta\%\) of the maximal approximation error in the respective element. Classical superconvergence corresponds to the case \(\eta= 0\). A computer based approach of determining regions of \(\eta\%\)-convergence for the gradient in boundary problems for the Poisson equation is presented. Sensitivity to mesh topology is discussed. Several numerical studies are presented. The paper is the third in a series of three on superconvergence.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 720994
zbMATH Keywords: Laplace equation
zbMATH Keywords: numerical examples
zbMATH Keywords: superconvergence
zbMATH Keywords: finite element
zbMATH Keywords: computer based approach
zbMATH Keywords: gradient
zbMATH Keywords: Poisson equation
reviewed by: S. Leif Svensson
MaRDI profile type: Publication
full work available at URL: 0168-9274(94)00029-8
OpenAlex ID: W2049782910
cites work: Validation of recipes for the recovery of stresses and derivatives by a computer-based approach
cites work: \(\eta\%\)-Superconvergence of finite element approximations in the interior of general meshes of triangles
cites work: Q4076713
cites work: Superconvergence and Reduced Integration in the Finite Element Method
cites work: Superconvergence of the gradient of finite element solutions
cites work: Some mesh schemes for quasi-linear elliptic equations
cites work: Superconvergence of the gradient of Galerkin approximations for elliptic problems
cites work: On superconvergence techniques
cites work: Asymptotically Exact Error Estimators for Rectangular Finite Elements
cites work: The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
cites work: The superconvergent patch recovery (SPR) and adaptive finite element refinement
cites work: Analysis of mixed finite element methods on locally refined grids
cites work: Q3126804
cites work: 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
cites work: Asymptotically exact a posteriori error estimator for biquadratic elements
cites work: Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
cites work: Recent experiences with error estimation and adaptivity. II: Error estimation for \(h\)-adaptive approximations on grids of triangles and quadrilaterals
cites work: Interior Estimates for Ritz-Galerkin Methods
cites work: Maximum-Norm Interior Estimates for Ritz-Galerkin Methods
cites work: Interior Maximum Norm Estimates for Finite Element Methods
cites work: Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 1
cites work: Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 2, Refinements
cites work: Q3126803
cites work: Performance of the h–p version of the finite element method with various elements
cites work: Pollution-error in the \(h\)-version of the finite-element method and the local quality of a posteriori error estimators
description: scientific article; zbMATH DE number 720994