Journal ArticleDOI
Element by element a posteriori error estimation of the finite element analysis for three‐dimensional elastic problems
Hideomi Ohtsubo,Mitsuru Kitamura +1 more
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This article is published in International Journal for Numerical Methods in Engineering.The article was published on 1992-06-30. It has received 21 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.read more
Citations
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Journal ArticleDOI
Validation of A-Posteriori Error Estimators by Numerical Approach
TL;DR: In this article, a numerical methodology which determines the quality (or robustness) of a-posteriori error estimators for finite-element solutions of linear elliptic problems is described.
Journal ArticleDOI
A variational method for finite element stress recovery and error estimation
TL;DR: In this paper, a variational method for obtaining smoothed stresses from a finite element derived non-smooth stress field is presented, based on minimizing a functional involving discrete least-squares error plus a penalty constraint that ensures smoothness of the stress field.
Journal ArticleDOI
Preconditioned conjugate gradient methods for three-dimensional linear elasticity
J. K. Dickinson,Peter Forsyth +1 more
TL;DR: Various preconditionsing methods are developed for use in preconditioned conjugate gradient iterative solution techniques and incomplete factorizations based on levels of fill, drop tolerance, and a two-level hierarchical basis are developed.
Journal ArticleDOI
Error estimates and adaptive finite element methods: A bibliography (1990‐2000)
TL;DR: Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view.
References
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Journal ArticleDOI
A simple error estimator and adaptive procedure for practical engineerng analysis
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
Journal ArticleDOI
A‐posteriori error estimates for the finite element method
Ivo Babuška,Werner C. Rheinboldt +1 more
TL;DR: In this article, a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements.
Journal ArticleDOI
A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis
TL;DR: It is shown that an extremely high rate of convergence is reached in practical problems using p-convergent methods, and applications to realistic stress analysis and potential problems are presented.
Journal ArticleDOI
Toward a universal h-p adaptive finite element strategy, part 2. A posteriori error estimation
TL;DR: In this paper, five different techniques for a posteriori error estimation of adaptive finite element methods for linear elliptic boundary value problems are presented, referred to as the residual estimation method, the duality method, subdomain residual method, a method based on interpolation theory, and a post-processing method.
Journal ArticleDOI
The hierarchical concept in finite element analysis
TL;DR: It is shown that it is possible to use the hierarchical concept for finite element shape functions to construct a range of error estimators which compare well with alternatives and are ideally suited for adaptive refinements of analysis.
Related Papers (5)
Element by element a posteriori error estimation and improvement of stress solutions for two‐dimensional elastic problems
Hideomi Ohtsubo,Mitsuru Kitamura +1 more
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
A simple error estimator and adaptive procedure for practical engineerng analysis
O. C. Zienkiewicz,J. Z. Zhu +1 more