Journal ArticleDOI
η%-Superconvergence of finite element approximations in the interior of general meshes of triangles
TLDR
A new definition of superconvergence is introduced, which generalizes the classical idea of super Convergence to general meshes and can be employed to determine the regions of least-error in any element in the interior of any grid by using a computer-based approach.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1995-05-01. It has received 15 citations till now. The article focuses on the topics: Superconvergence & Volume mesh.read more
Citations
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A Posteriori Error Estimation in Finite Element Analysis
Mark Ainsworth,J. Tinsley Oden +1 more
TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.
Journal ArticleDOI
Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
Randolph E. Bank,Jinchao Xu +1 more
TL;DR: This work develops superconvergence estimates for piecewise linear finite element approximations on quasi-uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms and analyses a postprocessing gradient recovery scheme for general unstructured, shape regular triangulations.
Journal ArticleDOI
A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
TL;DR: In this paper, the authors studied the pollution-error in the h-version of the finite element method and its effect on the quality of the local error indicators in the interior of the mesh.
Journal ArticleDOI
Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
Randolph E. Bank,Jinchao Xu +1 more
TL;DR: This work develops a postprocessing gradient recovery scheme for the finite element solution, inspired in part by the smoothing iteration of the multigrid method and uses the superconvergent gradient to approximate the Hessian matrix of the true solution and form local error indicators for adaptive meshing algorithms.
Journal ArticleDOI
Computer‐based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equations
References
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Finite Element Analysis
B. A. Szabó,Ivo Babuška +1 more
TL;DR: In this article, the authors present a general solution based on the principle of virtual work for two-dimensional linear elasticity problems and their convergence rates in one-dimensional dimensions. But they do not consider the case of three-dimensional LEL problems.
Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this article, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes, which has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems.
Journal ArticleDOI
Finite-Element Analysis
R. H. Gallagher,D. S. Griffin +1 more
TL;DR: The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon as discussed by the authors, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this paper, the authors derived a theorem showing the dependence of the effectivity index for the Zienkiewicz-Zhu error estimator on the convergence rate of the recovered solution.
Journal ArticleDOI
Local and global smoothing of discontinuous finite element functions using a least squares method
E. Hinton,John S. Campbell +1 more
TL;DR: In this article, the concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced, and the relationship between local smoothing and the reduced integration technique is established.
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The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
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O. C. Zienkiewicz,J. Z. Zhu +1 more
The superconvergent patch recovery (SPR) and adaptive finite element refinement
O. C. Zienkiewicz,J. Z. Zhu +1 more